The Dihner Lihrary
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CANON MATHEMATICYS,
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ljj|m€aiiomon triangulorum laterum rationalium: vna cum
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XXI
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XV
XIIII
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VIII
VII
VI
V
IIII
III
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♦
SCXVF
JRJM.AC
SECVUVi^S
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LXXXVI.
nuum
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FERJJPHIRIA
dati
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II
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V
VI
VII
VIII
IX
X
XI
XII
XIII
XIIII
XV
XVI
XVII
XVIII
XIX
XX
XXI
XXII
XXIII
XXIIII
XXV
XXVI
XXVII
XXVIII
XXIX
XXX
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Tuangvli Plani Rigtangyli
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LIX
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LVII
LVI
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LIII
LII
1 9
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XLIX
XLVIII
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XLIIII
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XXXIX
XXXVIII
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XLIX
L
LI
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B» E $ I V A
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congrua
I +9 Q
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LX
LIX
lviii
LVII
LVI
LV
LIIII
LIII
LII
LI
L
XLIX
XLVIII
XLVII
XLVI
XLV
XLIIII
XLIII
XLII
XLI
XL
XXXIX
XXXVIII
XXXVII
XXXVI
XXXV
XXXIIII
XXXIII
XXXII
XXXI
XXX
nuum
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SECFND^T
se it/ £
Fxcundifsiffioquc
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.XXXI
j PART.
congrua i
BaG
iss i s» r A
dati
lo ad- “
A*/** Perpendiculum
IOO, 000
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Hypotenufa
IOO, 000
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Perpendiculum Hypotenufa
100,000
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I Perpendiculo
1 .PgR.lFHSK.IA
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nufe coo«
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circuli xc.
pait. Angti
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nular con-
gruus,
Circa-
commo"
PER.IPHIS.IA
Perpendiculo
congrua
P A R T.
VIII.
S C RV P.
XXX
XXXI
XXXII
XXXIII
XXXIIII
XXXY
XXXVI
XXXVII
XXXVIII
XXXIX
XL
XLI
XLII
XLIII
XLIIII
XLV
XLVI.
XLVII
XLVIII
XLIX
L
LI
LII
LIII
LIIII
LV
LVI
LVII
LVIII
LIX
LX
congrua
E ali •
USIO V A
dati
lo ad-
SEV , AD TRIANGVLA .
Triangvli plani rlctangyli
Hypotenujk
100, 000
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Bafis
100,000
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100, 000
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E CANONE FiECVNDO
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nuum
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s E xj e
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TERTI yC
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LISIDM
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14, 78 l
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669, 1 16
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XXIX
XXVIII
XXVII
XXVI
670, 62 f
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XXII
664, 9 o 2”
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XIII
XII
XI
X
LX
VIII
VII
VI
V
IIII
III
II
I
4
TERTI
Fa?aindi(sim&que
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lut ie<aut.
part. Anga
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circuii xe,
psri.Angu
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gruus.
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PER.IP HERIA
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congrua
PART.
IX.
S C RVP.
Canon mathematicvs,
K 1 A N G V L I LANI ECTANGVLI
I
II
III
IIII
V
VI
VII
VIII
IX
X
XI
XII
XIII
XIIII
XV
XVI
XVII
XVIII
XIX
XX
XXI
XXII
XXIII
XXIIII
XXV
XXVI
XXVII
XXVII I
Hypotenujk
IOO, OOO
Perpendiculum Bajis
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nuum
XXIX
XXX
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CVND^C
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dati
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Bafi
congrua
LX
LIX
LVIII
LVII
LVI
LV
LIIII
LIII
LII
LI
L
XLIX
XLVIII
XLVII
XLVI
XLV
XLIIII
XLIII
XLII
XLI
XL
XXXIX
XXXVI
XXXV
XXXIII
XXXII
XXXI
XXX
nuum
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Bajis Perpendiculum
IOO, OOO
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SECrND^ff
SEK.IE
Fsecundifsimoque
E CANONE fICVNDO
Bajis Hypotenujk
IOO, OOO
Perpendiculum
TERJT1
Fascundifsimoque
E CANONE FICVNDo
Perpendiculum Hypotenujk
IOO, OOO
Bajis
SCRTP.
LXXX .
P ART.
congrua
Perpendiculo
Per.ipheh.ia
coramo
Circu-
gruus.
nulk con-
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part.Angu
circulixe.
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ipart.Angu
Ius reftus,
Hypotc-
.nufz con-
gruus.
Triangvli lani Rectangvli
commo-
PERIPHERIA.
Perpendiculo
congrua
Hypotenuft
1 . 00,000
Perpendiculum Bafis
Bafis
100 , 000
Perpendiculum Hypotenuft
Perpendiculum
IOO, 000
Bafis Hypotenuft
PART.
E CANONE SI-
E CANONE FAECVNDO
Faecundiffimoquc
S E Ii_l E
E CANONE FACVNDO
Faecundiffimoquc
IX.
nuum
S C RV ?.
SECFND^f
TE xpr I j£
lo ad-
dari
M flBVA
Bafi
congrua
XXX
XXXI
XXXII
XXXIII
XXXIIII
XXXV
XXXVI
XXXVII
XXXVIII
XXXIX
XL
XLI
XLII
XLIII
XLIIII
XLV
XLVI
XLVII
XLVIII
XLIX
L
LI
LII
LIII
LIIII
LV
LVI
LVII
LVIII
LIX
LX
congrua
Bafi
KZSIDYA
dari
lo ad-
x 6, 5 o 5 | 98, 62.8 6 ;; 1 d, 734
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100 , 000
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id, 7d4
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42,597
* 7
102 , 5 14 d
fi 8
102 , 52 I 4
i *
22,628
y 0
22 , 65 8
7
102 , 5 28 i
' fi s
102 , 534 9
22 , 689
« 0
42,719
* 7
102 , 541 d
fi 8
102 , 548 4
» *
44 , 750
» «
22 , 781
fi s
122, 555 Z
fi 8
IO 2 , 5 6 z 0
22 , 8 l I
1 1
22 , 842
fi 8
102,568 8
fi 8
102,575 d
5 0
22 , 872
f »
22 , 903
fi 8
102 , 582 4
<r \§
102 , 589 3
i »
22 , 934
S 9
22 , 964
6 8
102 , 596 I
fi 8
102 , 602 p
y s
22 , 995
y *
23 , 026
fi 9
102,608 pr
fi 8
102,616 6
y =>
2 3 = 05 *
1 *
23,087
6 9
102,623 5
«r 9
102 , 63 0 4
451=071
6xo
45 0,451
<5 19
449=832
6 l 7
449= 215
* * f
448, 600
« 1 4.
447,98 6
6 I X.
447 = 374
6 I o
44 *= 7*4
eo 9
44 *= 15 5
fi o 8
445 = 547
« 0 f
444 ’ 944
fi o
444 = 3 3
1 S O J
443=73 5
fi o I
443=134
<5 o O
442, 5 34
f 9 8
441 , 93 *
s 9 6
44 i= 340
_46i 023
6 o f .
461, 41 8
<5 o 4
460, 8 14
O X,
46 o, 2x2
O' I
45 9, <5 11
f 9 9
45 9*012
f 9 7
458,414
S 9 r
457 = 819
5 9 +
457 = £45
r s> j
45 *= *3 4
f 9 0
45 < 7 , 042
f
455=453
I M
4 54 = 8*5
XXX
XXIII
XXII
s 9 r
440= 745
f S> }
440, 154
S 9 x
439 = 5 *o
y 9 *
_43 8, 9*9
"TTf
43 8, 381
x 8 8
437 , 793
f 8 6
437= 207
y s 4.
43 *= * 4 3
y « »
43*= 040
43 5 = 459
y 8 o
434 ’ 879
y 7 9
434 ’ 3oo
y 7 r
43 3 ’ 74 3
57«
43 3 ’ 147
y » 7
454 ’ 478
y s *
_45 3 ' *9 3
y » 1
45 3= ito
<1 8 x
45 4 , 54 8
y 7 9
45 i» 949
y 7 »
451= 3 7 1
y 7 «s
450,795
57 «
450= 4 19
y 7 j
44 9 , 64.6
57 +
449, 072
y 7 1
448 = 501
y 7 1
447 = 93 0
y <r 9
447 = 3 * 1
y «*7
44 *= 794
y * y
446, 229
5 « +
44 5 = 6” 6 5
y « *
445 = 103
. r * *
444 = 54 i
SECFNDsf
SER^lE
Fsecundifsimoque
E CANONE EjECVNDO
Bafis Hypotenujk
100, 000
Perpendiculum
Fiecundiflimoque
E CANONE F 1 CVNDO
Perpendiculum Hypotenujk
100,000
Bafis
congrua
Perpendiculo
FXa.iruis.lA
commo-
Circu-
gruus.
nufae con-
Hypote-
lus redtui.
part.Angu
circuli xc.
Quadrans
riangvli Plani R ECTAN G VLl
Quadrans
circuli xc.
part.Angu
Ius r&3us,
Hypote-
nufrc con-
gruus.
Circu-
commo-
peb.ipher.ia
Perpendiculo
congrua
P ART.
XIII.
S C RVP.
I
II
III
IIIX
y
vi
VII
VIII
IX
X
XI
XII
XIII
XIIII
XV
XVI
XVII
XVIII
XIX
XX
XXI
XXII
XXIII
XXIIII
XXV
XXVI
XXVII
XXVIII
XXIX
XXX
congrua
BdlL
S- l S l D V A
dati
Io ad-
C‘J N 0 'N eJW ATHE M ATI CVS,
RIANGVLI LANI ReCTANGVLI
Hypotenufa
IQO, OOO
Perpendiculum Bajis
E CANONE Si-
nuum
P R r M
ffjma
nuum
E CANONE SI-
Bafis Perpendiculum
IOO, OOO
Hypotenufa
2 2, 49 f
97,437 0 |
X f
24 5 2 3
* 9
22, 5 5 2
97 » 43 ° S
97 » 4 2 3 P
a. i*
22, 5 80
i S
2 2, 608
6 tf
97 » 4 I 7 3
97, 410 8
i 9
22, 657
x s
22, 66 5
6 6
97,404 2
s s 1
97 » 397 *
X s
22, 695
& « 3 »
22, 722
0 «S
97 » 391 0
^ & 1
97 » 384 4
x 8
22, 750
* 8
22, 778
6 «S
97 » 377 S
tf tf
97 » 3 7 1 *
i ?
22, 807
22, 835
S 7
97 » 3*4 5
tf tf
97 » 3 57 9
% 8
22, 863
*• 9
22, 892
97 » 351 2
97 » 344 *
a. S
2 2, 920
% s
22, 948
6 7
97 » 3 37 9
fi fi
97 » 3 31 3
& 9
22, 977
4 s
2 3 , 005
* 7
97 » 3 2 4 *
a- 7
97 » 317 9
1 8
23,03 3
i 9
23,062
, « 7
97 » 3 ** 2
fi y
97 » 304 5
S S
2 3, 090
i £
23 , Il8
tf T
97,197 8
fi y
97 » 2 9 1 1
% 8
2 3, I46
s 9
2 3 » 175
i 9 s
97 » 284 3
fi y
97 » 177 6
a 8
2 3, 203
s. 8
23, 23I
fi y
97 , 1 70 j>
fi 8
97, 264 i
» & 9
2 3 , 2 6o
i S
23,288
6 8
97 » 2 5 7 3
« 7
97» 250 d
2 3 » 3 I 7
1 *
2 3 » 345
« s .
97,243 8
fi s
97 » 2 37 0
Bajis
IOO, OOO
Perpendi iulum Hypotenufa
E CANONE F£CVNDO
Fxcundiifimoqiic
iEKje
S KC y N n A
_ 2 Jjo 8 7
i O
23» 117
* i
33, 148
2 3 » *79
* ®
2 3, 209
23, 240
? *
23» 271
2 3 » 301
? I
2 3 > 3 3 2
t 1
23, 363
23» 393
i r
23,424
2 3»455
2 3 » 48 5
* <
2 3, 5 16
2 3 » 547
2 3 » 573
i o
2 3, 608
* r
2 3, 6 % Q
2 3» *7°
l *>
2 3 , 700
2 3 » 73 i
5 a
23 » 7 * 1
2 3 » 792
I «
23^823
2 3» 854
23,885
i 1
23 , 9 16
S o
23» 94 *
2 3 » 977
i »
24, 008
102, 630 4
<S 9
102,637 3
<5 «a
102, A44 i »
~6 9
102, 55 I I
« 9
10 2, 658 o
6 9
10 2 , ££4 P
7 e
10 2 , #71 p
s 9
102,678 8
1 o 2, 6 8 6 8
7 e
102, ^92 8
7 o
102,699 8
7 a
102, 706 8
7 «
102,713 8
7 e
102,720 8
7 »
102, 7278
102,734 8
7 *
102,741 ^
a
102, 748 9
7 1
102,756 o
7 1
102,763 I
7 s
10 2, 770 2.
102,777 3
7 *
102, 784 4
7 1
102,791 5
7 *
102, 798 S
0 * *
102,805 7
7 J
102, 8 12 O
7 *
102, 820 9
7 4
102, 827 z
7 *
102, 834 3
_ 7 * .
102, 84I 5
SECVND^f
S E RJ E
Faecundifsimoque
E CANONE FrECVNDO
Bajis Hypotenufa,
100 , OOO
Perpendiculum
Perpendiculum
IOO, 000
Bafis Hypotenufa
E CANONE FrECVNDO
Fatcundiflimoque
TER Tf A
.
! 43 3 » 147
t 7 +
43 2 » 573
y 7 t
452,001
y 7 1
43 1 » 43 °
y 7 0
430, 860
y «s 9
430, 291
y « 7
429, 724
y fi y
429, 159
,y 6 +
4 2 8 , 595
y fi y
428, 052
y fi »
427,471
f tf 0
426, 911
y y 9
42*, 352
y y 7
4 2 5 » 795
y y «
4 2 5 » 239
y y +
424»*85
y y j
424, 132
y y 4
423, 580
y y 0
423» 030
y + 9
422,481
y 4- ?
421, 933
y 4- fi
421, 387
y + y
420, 842
y + *
420, 298
y + ^
419, 756
y + «
419, 2 I 5
y 4 0
418, 675
y j 8
418, I37
y » 7
417, 600
y i fi
417, 064
y ? +
41*, 530
dati
USI 9 YA
Bafi
congrua
44 4, 541
V 9
443, 982
443*424
s s “
442, 8 68
H 5
442 , 312
f ? ?
441, 759
f s t
441, 207
f y o
440, 656
f + 9
4 40, 107
S 4- *
43 9 » 5 59
y ■* 7
43 9 » 012
V 4
438, 467
y + +
43 7 » 9*3
t + ‘
437» 381
y + *■
4 3*» 83 9
y j 9
43 *» 300
y j 9
.43 5» 7*1
y ? 7
435 » 224
y i y
414*8 9
y 3 *
434 155
y i 1
43 3, 622
y i -
43 3 » 090
y » o
43 2 » 5*o
y 1 9
43 2 » 03 1
fi?
43 i» 503
y » fi
430,977
y i y
430, 45 2
y 1 s
429, 929
y 1 i
42 9, 406
428,^886
f X o
42 8, 3 **
LX
LIX
LVIII
LVII
LVI
LV
LIIII
LIII
LII
LI
L
XLIX
XLVIII
XLVII
XLVI
XLV
XLIIII
XXXIX
XXXVIII
XLIII
XLII
XLI
XL
XXXVII
XXXVI
XXXV
XXXIIII
XXXIII
XXXII
XXXI
XXX
TERTl^t
Faecundiflimoque
s c r v p.
Lxxvr.
E CANONE F1CVNDO
Perpendiculum Hypotenufa
IOO, OOO
Bafis
P ART.
congrua
Perpendiculo
PERIPHERIA
commo-
Circu-
gruus.
nulie coi
Hypote-
lus re&i
part.An;
circuli x
Quadrat
Tr iangvli Plani Rectangvli
SEV, AD TRIANGVLA.
Triangvli Plani Rectangvli
Orcu-
Quadrans
circuli xc.
part. Angu
Ius re&us,
Hypote-
nufs con-
gruus.
comma-
1 PER.IPHES.XA
Perpendiculo
congrua
Hypotenufa
IOO, 000
Perpendiculum Bafis
Bafis
100,000
Perpendiculum Hypotenufa
Perpendiculum
100, 000
Bafis Hypotenufa
diti
Rl S ID VA
Bali
congrua
.
i PAR.T.
E CANC
)NE Si-
nuum
t M A
E CANONE FaECVNDO
Fxcundifsimoquc
SE.H.IE
SE C VH D-yj€
.E CANONE F1CVNDO
Faecundifsimoque
TERTIA
XIII.
p tt
SCRVP.
j
|l XXX ,
23, 345
97,237 0
24, 00 8
102,841 y
41*’ 5 3 O
428, 3 ** ,
XXX
XXXI
XXXII
t s
373
i K
23 , 40 !
* S
97,230 i
fi 8
97,223 4
? *
24,039
j 0
24, 0*9
V 1
102,848 7
T X
102, 855 9
S i $
4 1 5 , 997
1 ) X
4 I 5 ’ 4*5
S ‘ «
42 7, 848
y , 7
4 2 7 ’ 3 5 *
XXIX
XXVIII
XXXIII
XXXIIII
t 8
23,429
J- 9
23,458
& 8
97,21* 6
(S #
97, 209 8
f i
24, 100
» *
24, 1 3 1
7 *
102, 8*3 X
7 x
102, 870 3
r 1 1
4 X 4 ’ 9 34
f x 9
4 I 4’40 5
.£ x a
42*, 81 5
s i y
42*, 3 00
XXVII
XXVI
XXXV
XXXVI
i 8
2 3, 48*
1 s
23, 5i4
« 9
97, 2 02 9
«S 8
97 , 19* i
» *
24, 1*2
* *
* 4 ’ 19 3
7 *
102, 877 5
10 2, 884 8
S 1 8
4 1 3 > 877
S » 7
4 1 3 ’ 3 5 0
V ‘ J
425 ’ 7S7
y i 1
425’ 275
XXV
xxim
XXXVII
XXXVIII
x 3
23 » 54 2
s 9
23 ’ 57 i
fi 8
97, 189 3
& 9
97’ 182 4
? 0
24, 223
* »
24, 254
7 S
I02i892 I
7 J
102, 8994
X 1 *
412,825
? X 4
412, 301
y 1 0
424, 7*5
y 0 9
424, 25*
XXIII
XXII
XXXIX
XL
i s
23 ’ 599
1 8
23, 627
fi 8
97,175 6
<s 9
97’ i*8 7
i *
24, 285
i *
24, 3 i *
7
10 2, 90* *
7 *
102, 913 8
411,77$
F X J.
411,25*
y 0 3
423, 748
y 0 7.
423 > 241
XXI
XX
XLI
XLII
% 9
23 ’*$*
% s
2 3, 684
s 9
97, 1*1 8
* 9
97 ’ 154 j>
24, 347
i °
24 ’ 3 77
7 i
102,921 I
7 J
102, 928 4
S X 0
4 10 ’ 7 3*~
f * 9
410, 217
y 0 6
422,735
S « J
422, 2 3 0
XIX
XVIII
XLIII
XLIIII
i 8
23,712
*. 8
2 3, 74O
* 9
97, 148 0
fi V
97 ’ 141 1
j i
24, 40 8
i 1
24,439
io2, 93 5 ? 7
7 ?
102,943 0
y * 8
409**99
s «i 7
409, 182
y 0 f
421 , 727
5 0 x
421, 225
XVII
XVI
XLV
XLVI
% g>
2 3 > 769
l s
2 3 ’ 797
6 9
97’ 134 1
6 9
97’ 127 3
i »
24,470
t *
24, 50 1
7 j
102,950 3
102,957 7
„ S 1 f
408, **7
_ y * 4
408, 15 3
y 0 i
42 0,. 7 24
4 V 9
420, 225
XV
XIIII
1
XLVII
XLVIII
X S
23, 825
X 8
23 ’ §53
<s 9
97’ 120 4
97 ’ 113 4
s *
2 4 » 5 3 2
j 0
24 ’ 5*2
7 j *
102,9*5 0
7 +
102, 972 4
s » i
407, *4o
y ‘ X
407, 12 8
4 9 3
4 I 9’727
-i- 9 7
4 r 9, 230
XIII
XII
XLIX
L
23, 882
23,910
<5 9
97’ 10* 5
T 0
97 ’ 099 5
s *
24 ’ 593
* »
24, *24
102,979 7
7 +
102, 9871
s » »
40*, *I7
y 0 9
40*, I08
„ 4 - 9 <S
4 i 8 ’ 733 -
418,2 39
XI
X
LI
LII
1 S
23 ’ 93 8
x 8
23, 9**
fi 9
97 , 092 *
7 0
97,085 6
i t
24, *5 5
e x
24, *8*
102,994 s
7 +
103, ool 9
S 0 8
4 ° 5 > *oo
y 0 7
405, 093
4 9 4
4 X 7 ’ 745
4I7, 2 5 2
IX
VIII
VII
VI
LIII
LIIII
x 8
23, 994
* 9
24, 02 3
7 0
97,078 *
fi 9
97 ’ 071 7
. * *
24 ’ 7 I 7
j o
24 ’ 747
7 4
103,009 3
7 il-
IO 3, 01* 7
f r»
404, 587
» ° s
404, 082
491
41*, 7*1
4 9 0 ,
41 *, 271
LV
LVI
X $
24, 05 1
x 8
24, 079
7 0
97,0*4 7
7 0
97 ’ °57 7
24, 778
* *
24, 809
7 4
103, 024 1
7 T
103, 03 I d
y 0 4,
403,578
5 0 x
403,07*
4 8 9
415 ’ 7S2
4 3 3
4 I 5’294
4 3 fi
414, 808
4 3 y
414, 323
V
un 1
LVII
LVII 1
x 8
24, 107
& 9
24, I 3 <7
7 0
97’ 050 7
7 *
97,043 *
24, 840
24, 871
7 4
103,039 O
' 4 -
1 0 3, 04* 4
y 0 j
402,575
y 0 0
40 2 ’075
III
11
LIX
LX
x 3
14, 164
x 8
24, 192 1
7 0
97’ 03* 8
7 0
97,029 <?
j *
24, 902
2 4, 9 3 3
103, 05 3 ^
7 r
103,0*1 4
& 9 9
401,57*
* M
401,078
4 S }
41 3, 840
4 » i
413’ 357
I
♦
tHJMvtS
tiuutn
E CANONE SI-
S E C r N D st I
$£ HJ E
Fxcundifs inioque
E CANONE FjECVNDO
T E KJT l y
Fsmindifsimo
E CANONE
SCRVP.
LXXVI.
ane — ~ — .
F 1CVNDO
P As.1,
;ruus.
lufar con-
-Jypo te-
ns redus.
rarr. Angu
circuli xc
Quadram'
congrua
Sali
USIDYA
dati
j
Bajis Perpendiculum
100, 000
Hypotenufa
Bafs Hypotenufa
100, 000
Perpendiculum
Perpendiculum Hypotenufa
100, 000
Bafis
congrua
Perpendiculo
PEriphzria
commo- :
* 4lw "
Circu- ■
T RIANGVLI LANI RECTANGVLI
Quadrans
circuli xc.
J>art. Angu
Ius reftus,
Hypote-
nulie con-
gruus.
Circu-
colurno-
JSR.iyHSS.IA
Perpendiculo
congrua
PART.
XIIII.
SCRVP,
I
II
III
IIII
V
VI
VII
VIII
IX
X
XI
XII
XIII
XIIII
XV
XVI
XVII
XVIII
XIX
XX
XXI
XXII
XXIII
XXIIII
XXV
XXVI
XXVII
XXVIII
XXIX
XXX
CANO'N zMATHEMAncrs,
RlANGVLl LANI R ECTANGVLI
Hypotenujk
loo, ooo
Perpendiculum Bafts
E CANONE Si-
nuum
F KJ M
M 24 , 192
97 , 029 6
■ 1 ^ in
24,220
x 9
24 , 249
7 i
97,02 z 5
7 e»
97,015 5
j. 8
24 , 277
io
24 , 305
7 1
97.00 8 4
7 0
97.001 4
x 8
24 , 3 3 3
i 8
24 , 36 T
7 1
96,994 3
7 *
9 6 , 9 8 7 z
1 6
24 , 390
i 8
24 , 418
7 S
96,980
7 1
96,973 O
1 S'
24 , 446
% S
7 l
96,965 9
96,958 8
i*s>
24 , 503
24 , 5 30
7 1
9 *, 95 * 7
7 1
96,944 5
* 9
* 4 .ff?
, 4 . 1_?7
7 " 8
96 , 93 ^ 4
9^,930 3
X . 5 “
i 4 , « 1 j
•7 X
96,923 1
9 *, 91 5 — P
i »
24 , gj -2
24 , 700
y r _
96,908 8
7 %
$ 6 , 901
24,728
24 , 75 «
T ■ ■ 'i
96,894 4
/ i
9 6 , 8 8 7 z
j, g
24 , 783 .
24 , 81 3
9 6, 8 8 0 0
7 *
96, 87 2 8
i #
24 , 8 4 ?
, * s
24 , 869
96 , 865
9^,858 3
24 , 9 Z 5
~f ~T~
96,851 I
96,843 8
2 + 9 \i
24 , 98 z
7 \
96 , 8 36 6
7 i
96,829 3
X 8
2 5,010
i 8
25, 03 8
$
96,822 0
96,814 §
Bajis
IOQ, OOO
Perpendiculum Hypotenujk
E CANONE MCVNDO
Faecundifsimoque
SZBJ-E,
SSCrND A
24 , 9 3 3
? *
24 , 9 <54
i 1
_ 1 +>_ 99 S
? 1
15,026
i a
2 5,056
i I
25, 087
»
25, 1 1 8
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25 , 14 9
i 1
25,l8o
i i
25, ZII
i 1
2 5 , 2 - 4 2 ,
Yo
2 5 ’ 1 7 ^
i i
2 h 3 P 1
105,061 4
7 4
103, o 68 8
7 a
J 03, 076 3
7 f
103,083 8
7 r
103 , 091 3
7 f
103,098 8
7 «
10 3 , 1064.
7 *
103 , 11 3 ^
7 «r
103,121 5
? 1
25, 3 34
; 1
2 5 , 3.^1
* 5 > 39 *
? *•
25,428
5 1
25 , 45 ^
2 49.0
r>
25 , 521
» *
2 5 » 3 5 2
25 ,*; 14
i I
2 5 , *4 5
* t
25 , 676
« 1
25,707
* *
25, 73 8
5 *
25 , 769
* *
25 , 800
j *
25 , 831
* 1
25 , 862
7 y
103,129 o
7 fi
103 , 136 " 6
I0|, 14^
1 0 3 ,, x 51 8
7 fi
2
«■
■7 r*
103 , 159 £
103,16 7 _o
7 — TS-
103,174 f
I 03 , l 82 _z
103,189 8
7 7
103, 197^5
IO 3, 20 | 1
10 3,2 12 8
I 03 , 220 <
7 7
103,2 28 z
Io 3 > 2 3 5 |
103,243 d
7 7
103,251 3
7 7
103,259 O
7 7
103,266 7
103,274 ?
7 7
103,282 z
7 8
103,290 O
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104,843 3
104,852 p
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317, 481
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317, 159
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3 32, 858
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Triangvli Plani Rectangvli
lx
LIX
LVIII
LVII
LVI
LV
XIIII
LIII
LII
LI
L
XLIX
XLVIII
XLVII
XLVI
XLV
XLIIII
XLIII
XLII
XLI
XL
XXXIX
XXXVIII
XXXVII
XXXVI
XXXV
XXXIIII
XXXIII
XXXII
XXXI
XXX
II
IljMsA
SECFND^t
t e aj s
Fscundifsimopiie
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TEXTIS
Fimindifsimoquc
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j
flUUtti
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) 0
COIJglUH
Biiti
a. a s L d Y A
dari
Bajis Perpendiculum
IOO, ooo
Hypotenuja,
Bajis Hypotenuja
IOO, ooo
: Perpendiculum
Perpendiculum Hypotenuja
IOO, ooo
Bajis
SCSVP,
LXXII.
PAs.1.
congrut
Perpendiculo
?EJUPHSSUA
commo-
Circu-
gruui.
nufx eotw
Hypote-
lus reiShi*.
pare. Angn
circuli xc.
Quadram
SEV, AD TRIANGVL A.
! Qutdnns
circuli xc.
ip*rr. Angu
Jui reflui,
.Hypote-
mufa; cou-
jruus.
, GYcu-
T R iANGVLI P; lani .Rectangvli
fcommo-
Perpendiculo
congrua
'
Hypotenufa
10 0,000
Perpendiculum Bajis
Bajis
100,000
Perpendistdum Hypotenufa
Perpendiculum
IOO, ooo
Bajis Hypotenufa
PART.
XVII.
ScRYP,
E CANONE Si-
nuum
pst r
E CANONE FICVNDO
Ixcundifllmocjuc
sziiiz
SV.CVND A
E CANONE FACVNDO
fxcundiffimoque
lo ad-
daci
R1JIT3YA
Bafi
congrua
I
II
III
II II
V
VI
vir
VIII
IX
x
XI
XII
XIII
XIIII
XV
XVI
XVII
XVIII
XIX
XX
XXI
XXII
XXIII
XXIIII
XXV
XXVI
XXVII
XXVIII
XXIX
XXX
congrua
Bafi
R. E S I D V A
dati
lo ad-
CANON fJxC athe m aticvs.
TRIANGVII PLANI ECTANGYLI
circuli xc.
patr. Angu
Ius reftus,
Hppote-
sufe con-
gruus,
sommo" 1
P8R.IPK ES.IA I
Perpend iculoj
congrua 1
Hypotenuja
loo, ooo
Perpendiculum Bajis
Bajis
100,000
Perpendiculum Hypotenuja
Perpendiculum
100 , ooo
Bajis Hypotenuja
r
P A R T. 1
XVIII.
S C R v F.
E CANONE Si-
nuum
tUlMjt
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faEcundifsimdquc
S EKJ £ '
1 ■? S C r AT D
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Excundifsimorjue
TEKTI.A
Io ad-
3L* S!Dr*
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congrus
50, 902
95 , 105 7 !
32,492
105, 146 z
3 07, 768
3 2 3, 607
30, 929
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3 0, 95 7
95 , 096 7
95,087 7
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307, 464
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31,012
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30«, §57
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306, 554
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322,740
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31, 040
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105, 196 1
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105, 206 1
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3 06, 252
305, 950
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322, I65
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105, 2663
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316,255
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LX
LIX
LVIII
LVII
LVI
LV
LIIII
LIII
LII
LI
L
XLIX
XLVIII
XLVII
XLVI
XLV
XLIIII
XLIII
XLII
XLI
XL
XXXIX
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xoo, ooo
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xoo, ooo
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S C R-V P.
LXX I.
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Perpendiculo
PERIPHERIA
COfllfflO-
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part; Angrg
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Triangvli Plani Rectangvli
SEV, eAD TRIANGVLA.
Triangvli Plani Rectangvli
JiydrAEJ
'lirculixc.
sart.Angu
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IOO, 000
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Bafis
IOO, 000
Perpendiculum Hypotemfa
Perpendiculum
IOO, OOO
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PART.
E CANONE SI-
E CANONE FjECVNDO
E CANONE F 1 CVNDO
xvnr.
nuum
Fsccundiffimyqi}.?
s S BJ E
Fsecundiflimyque
S C R V P.
PRl MAt
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TE J{T /
load-
dati
1ISIOU
Baii
congrua
XXX
XXXI
XXXII
XXXIII
XXXIIII
XXXV
XXXVI
XXXVII
XXXVIII
XXXIX
XL
XLI
XLII
XLIII
XLIIII
XLV
XLVI
XLVII
XLV III
XLIX
L
LI
LII
LUI
LIIII
LV
LVI
LVII
LVIII
LIX
LX
JI± 7 J 0
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3 75 8
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3 i, 78 *
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XXIII
XXII
XXI
XX
XIX
XVIII
XVII
XVI
XV
XIIII
XIII
XII
XI
X
IX
VIII
VII
VI
V
IIII
III
II
I
♦
S C R V P*
fRlM^A
nuum
E CANONE SI-
SECFNDiA
SERJZ
Faecundiffim 6 auc
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Bafis Perpendiculum
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%,%% 1DYA
100, 000
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XXIX
XXVIII
XXVII
XXVI
XXV
XXIIII
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C^HON mathematicvs.
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corame-
Triangvli Piani Rectangvli
2 I 3 UPKS 1 U&
Pcrpcii4iculo
congrui . .
PA8.T,
XIX.
* C RTf.
I
II
III
IIII
V
VI
VII
VIII
IX
X
XI
XII
XIII
XIIII
XV
XVI
XVII
XVIII
XIX
XX
XXI
XXII
XXIII
XXIIII
XXV
XXVI
XXVII
XXVIII
XXIX
XXX
Hypotemfi
IOO, ooo
Perpendiculum Bajis
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congrua
congrua
Bafi
s-atia vi
dati
io ad»
PSJ M^€
nmim
E CANONE SI-
Bafis Perpendiculum
IOO, ooo
Hypotcnufa
SECFND^T
SE 11/ E
Faecundifsimoquc
E CANONE FACVNDO
Bajis Hypotemfa
IOO, ooo
Perpendiculum
TEHJl,^£
Fscundifsimoque
E CANONE F 1 CVNDO
Perpendiculum Hypotemfa
IOO, ooo
Bafis
Tr iangvli Piani Rectangvli
** y y ^ «fi* JL
* 7 4
290 , 147
T. i 7 "S -
289,873
1
^ S 9
3 06 , 896
l f 9
3 06 , 637
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289 , 6 00
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289 , 327
4 f 8
306,379
1 f S
3 06 , 12 I
474
289,055
288 , 78 3
4 f 7
305,864
4 f 7
305, 607
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2 8 8 , 5 I I
t 7 I
2 8 8 , 240
* 7 7
305 , 3 50
4 7 6
305, 094
17 *
287 , 970
170
287 , 700
4 7 7
3 04 , 8 3 9
477
3 04 , 5 84
170
287,430
1^9
2 87 , l 6 l
477 j
304 , 329
47 +
304 , 075
I 69
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16 8
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1 86 , 089
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303 , 315
4 7 j
303,062
107
z 8 5 , 82 z
l \6 7
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471
302 , 810
4 7 1
302 , 559
285,489
2 6
285,023
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302 , 308
4 7 *
302 , 057
1 5
284,758
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2 84 , 49 3
2 f O
30 I, 807
47 ®
3 01 , 5 57
2 84 , 229
16 i{.
283,965
4 4 . 9
301 , 308
4 4-9
3 01 » 05 9
4 6 ' J
283,792
4 6 J
283,439
300 , 8 lO
% 4 . 8
3 00 , 5 62
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283 , 176
t 6 Z
282 , 914
4 4 . 8
3 00 , 3 I 4
4 4 7
300 , O 67
2 2
28 z, 6 j 2
% 6 t
282 , 391
i 4 , 7
299 , 820
i 4 er
299 , 574
XX
LIX
LVIII
LVII
LVI
LV
LIIII
LIII
LII
LI
L
XLIX
XLVIII
XLVII
XLVI
XLV
XLIIII
XLIII
XLII
XLI
XL
XXXIX
XXXVIII
XXXVII
XXXVI
XXXV
XXXIIII
XXXIII
XXXII
XXXI
XXX
s cRvr.
LXX.
PAR.T.
congrua
Perpendiculo
EsKItmuiA
eommcs-
Circu-
gruu#.
nufx coim
Hypote- ■
lus rcdus,
part.Angu;
circuli xe.i
Quadras?;
SED, AD TRIANGVLA.
Quadrans] 1
circuli xc.j
part. Angu
Ius rectus
Hypotbc-
nuficcon'
gruus.
Circu»
coramo-
PER.IPHERIA
Perpendiculo
congrua
PAR-T.
XIX.
S C RY F.
XXX
XXXI
XXXII
jXXXIII
;xxxmi
XXXV
xxxvi
XXXVII
XXXVIII
XXXIX
XL
XLI
XLII
XLIII
XLIIII
XLV
XLVI
XLVII
XLVIII
XLIX
L
LI
LXI
LIII
LIIII
LV
LVI
LVII
LVIII
LIX
LX
congrua
Bafi
ft E S 1 O VA
dati
io ad-
T R I A N G V L I Pl ANI ReCTANGVLI
Hypotemfa
IOO, ooo
Perpendiculum Bajis
E CANONE Si-
nuum
VpiM yC
Bajis
IOO, ooo
Perpendmdum Hypctenuja
E CANONE FAECVNDO
FscundiiGmoque
se/^i e
SECV NDyf
33 > 3 ®i
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5 5, 408
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33,456
9 8
94 , 254 4
9 7
94, 244 7
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3 3,463
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5 5, 490
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94, 235 0
9 7
94, 2 2 5 3
i. i >
53, 518
1 7
3 3 , 545
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94 , 2 X 5 5
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94, 205 8
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3 3 , 573
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94 , I 47 I
7
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94 , 127 4
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94,078 z
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3 3 , 956
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33,983*
94 , 0 5 8 *
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94 , 048
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94,05 8 7
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94,028 8
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94, Ol 8 £
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93,979 *
93,969 3 !
nuum
E CANONE SI-
Baps Perpendiculum
I oo, ooo
Hypotenuja
SE&fNDJC
S E IU E . -
Facundiis imoque
E CANONE FAECVNDO
Bajis Hypotenuja
IOO, ooo
Perpendiculum
Perpendiculum
IOO, ooo
is HypotenufA
E CANONE FAECVNDO
Fsecundiflimoque
TE* TUA
Io ad-
daci
S.ISID VA
Bafi
congrua
! 3 5 , 4 x 2 | 106 , 084 8
3 5,445
j t
• 35,477
a 1 0
106,095 8
11 O
106 , 106 8
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3 5, 5 10
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3 5, 54?
I 0 9
106, 117 7
II 0
106 , 128 7
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3 5, 576
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3 5,608
106, 139 7
1 « 9
106 , X 50 6
i ; j
3 5,641
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3 5 , 674
10 0
Xo 6 , l 6 l 6
11 0
106 , 172 d
35,707
H
5 5,740
I 1 O
I 06 , 183 6
III
106 , I 94 7
i *
3 5, 772
_ * *
35 , 805
106 , 205 7
11 I
106, 2168
35,838
? ;
35, 871
11 I
IO 6 , 2 z 7 $
11 I
106 , 239 0
t i
35, 904
3 5, 937
1 1 1
106,250 I
1 1 1
106 , 261 z
? t
35, 969
j *
3 6 , 002
IX 1
106,272 3
11 I
106 , 283 4
i s
3 6 , 0 3 5
36 , 068
11 1
106 , 294 5
11 z
X 06 , 305 7
i s
3 <7, I O I
t i
36 , 134
11 I
106 , 316 8
11 X
106 , 328 0
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3 6 , 167
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36, 199
11 i ^
106 , 339 \Z
Iit
106 , 3 50 4
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3 6 , 2 6 5
I I X
X 06 , 361 6
II X
I 06 , 3 72 8
3 <5", 2 9 1
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t 1 X
106 , 384 0
X s i
106 , 395 3
s s
36 , 364
36,397
11 X
106,406 5
1 1 j
106,417 8
TERTI yC
Ficcundiflimoque
E CANONE FrECVNDO
Perpendiculum Hypotenujk
IOO, ooo
Bafis
282, 39X
299 , 5 74 !
% 6 l
2 82, 1 30
160
2 8 1, 870
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299, 328 j
t + * ■
299, 08 3 1
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281, 6x0
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281, 350
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298, 838
1 4. *
298, 593
1*9
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280, 8 3 2
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298, 349
1 4. 4.
298, 105
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280, 316
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297, 862
ifi
297, 6x9
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2 80, 05 9
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279, 802
141
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297, 135
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* 79 , 545
t -j «
279, 289
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296, 893
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296, 652
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279,033
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278 , 778
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296, 17 1
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278, 269
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295, 931
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295,691
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278, 015
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277, 761
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295,452
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277, 508
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294 , 975
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277, 002
1*1
276, 750
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2 94 ,A 99
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276, 498
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276, 247
M7
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275, 746
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293 , 5 5 3
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293, 317
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275,496
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275, 246
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293, 082
l * T
292, 847
1 4. 9
274, 997
1 4. n
274, 74S
i 5 4.
292, 61 3
2 92, 379
XXX
XXIX
i XX VIII
XXVII
XXVI
XXV
XXIIII
XXIII
XXII
XXI
XX
XIX
XVIII
XVII
XVI
XV
XIIII
XIII
XII
XI
X
IX
VIII
VII
VI
V
IIII
III
II
I
♦
S C R VP.
LXX.
PARC.
Triangvli Plani Rectangvli
congrua
Perpendiculo
PSR. 1 PHERIA
commo-
Circu-
gruus.
nufa: con-
Hypote-
lus re&us.
part.Angu
circuli xc.
Quadrans
CANON MCATHEMATIcrs,
Triangvli Plani Rectangyli
Ci * ca ~ _____ , . lo ad-
Quadrans
circuli xc.
part.Angu
lus re£tus,
Hypoce-
nufie con-
gruus.
commo*
PSR.XPHIR.XA
Perpendiculo
congtua
Hypotenufa
IQO, OOO
Perpendiculum, Bajis
Bafis
IOO, ooo
Perpendiculum Hypotenufa
Perpendiculum
IOO, OOO
Bafis Hypotenufa
dati
S. 1 «ISTA
Bafi
congrua
P ART.
E CANONES i-
E CANONE fjECVNDO
Sx eundi fs im 6 <ju e
t£\l£
SECFNDA
E CANONE JACVNDO
Excundiftinio^uc
TBMJTljt
■ uuum
s c a v’p. ^ I? L M A
♦
3 4 , 2 o a
93» 9*9 3
i
34, 229
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ii
i
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V
54» 5 59
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VI
% 7
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93 , 909 4
' VII
i 7
34* 395
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93» 899 4
VIII
i 8
34, 42 I
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IX
34,44§
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X
t 7
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34» 5 37
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34» 5 84
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1 8
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io 1
93» 819 1
XVI
34*3 9
/ leo
93 * 809 I
XVII
3 4, 666
93*799 °
XVIII
34» *94
93,708 p
XIX
1 7
34» 7 2 1
IO 1 ?
93* 778 8
XX
34» 748
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93» 7*8 7
XXI
34» 775
93,758 < 3 T
XXII
a 3
34 » 803
1 O I
9 3,748 5
XXIII
34» 830
IO 1
93,738 3
XXIIII
_ 1 7
34-85 7
10 s
93 , 728 i
XXV
34 » 884
10 l
93,718 I
XXVI
i s
34» 9*2
10 1
95,707 i>
XXVII
34» 93 9
I 0 1
93**97 8
XXVIII
34* 9**
10 z
91,687 6
XXIX
34» 9 9 3
1 0 z
9 5 > 677 4
XXX
1 *
3 5 * 02 1
I 0 1
9 3 » * * 7 1
congru»
Baii
S.ESIBVA
dari'
lo ad- '
TSJMJi
miam
E CANONE S I-
Bafis Perpendiculum
loo, ooo
Hypotemtfx
3 *» 397
10^,417 8
!l 274,748, 292,379
LX
3 *» 4 3 0
3 *» 4 * 3
3 *» 49 *
* s
3*, 529
»13
106,429 1
1 i i
I06, 440 4
a 4» 9
274,499
14«
2 74 » 2 5 *
» 3 3
292, 14 <5
* 3 3
291, 91 3
LIX
LVIII
* ■» 3
10*» 451 7
1 » 3
io<?, 463 0
148
274, 003
147
2 7 3 » 75 *
1 1 *
291, 68 1
i l' 3 »
291, 449
LVII
LVI
} i
3 *» 5 * 2
3 3
3 *» 595
11 j
106,474 4
1 1 9
106,485 6
147
2 73 » 5 °9
145
273, 263
a 5 1
291, 2 17
t f 1
290, 985
LV
LIIJX
3 6, 6 2 $
3 3
%6, 66 1
1 1 3
IO 6, 49* 9
1 1 4
io^, 508 3
146
273 , 0*7
1 4 fi
272, 771
1 j 1
290, 754
i 3 1
290, 523
LIII
LII
3 <£, ^94
3 *» 7 2 7
1 » 3
tlo6, 5196
106, 5310
i 4 y.
272, 52 6
» 4 y
272, 281
£ ^ O
290, 295
% j 0
290, 06 3
L 1
L
3 V
16,760
3 3
3 *» 79 3
1 1 4
io5, 542 4
I I 4,
io*, 553 8
^ 4 y
272, 036
144
271, 792
119
289, 834
1r % $
289,<>05
XLIX
XLVIII
36, §26
_ 3 s
36, 859
106, 565 i
1 1 4
T06 , 176 6
144
^ 71 , 54 <?
» 43
271, 305
s * 9
289, 376
»& 9
289, 147
XLVII
XLVI
3^,892
3 3
3 *» 9 2 5
106, 588 0
1 1 y
io< 5 , 5 99 <
1 4 j
271, 062
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270, 8 l 9
x l 8
2 88,9I9
1 * 7
288,692
XLV
XLIIII
3 *» 95 ^
3 3
3 *» 9 9 1
1 1 4
10 5 , 610 <>
* 1 y
106, 622 4
144
27O, 577
141
2 70, 335
1 1. 7
288, 4* 5
117
288, 238
. XLIII
XLII
37,024
3 7 » 0 5 7
i 1 f
106,633 jP
, 1 y
106,645 4
i 4 1
270, 094
1 4 1
269, 853
11 7
288, 011
z z <s
287,785
XLI
XL
37,090
$ 3
37 » 1 2 3
1 1 e
io 6, 6 $6 9
t 1 f
io< 5 , 668 4
141
2*9, <512
1 4 1
2*9, 371
1 1 fi
287, 559
S- 2 » y
2 87 » 3’?4
XXXIX
XXXVIII
3 4
37**57
3 3
37 » 190
t I
106, 680 0
1 1 *
106,691 f
1* 4 ©
2 *9, 131
1 3 9
268, 892
1 i y
287, 109
114
2 8 < 5 , 885
XXXVII
xxxvi
3 3
37 , 22 5
3 3
3 7 , 2 5 *
116
106,701 1
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106, 714 6
i 3 9
2 < 58 , 6 5 3
t } 9
2*8,414
286,661
'114
286,417
xxxv
XXXIIII
37 » 2 ^9
3 3
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1 1 «
IO 6, 726 2.
1 t 4
106,717 8
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2458, 15*5
l j s
2 *7» 9 3 7
1 1 4
286, 213
1 t j
285, 990
XXXIII
XXXII
37, 3 55
37, 3 ai
116 ,
IO <5, 74 J> 4
1 I 6
10 6, 761 0
j s- 3 8
2*7, <5-99
i 3 7
267,462
. 1 1 i |
2 8 5, 767
285» 545
XXXI
XXX
SEOFNDA
sek 1 e
Fasciitidi' {fi m 6 q ue
E CANONE FICVNDO
TEKjflA
9» 1 • nr *■
S C R V P.
LXIX.
rsecunauumuquc
E CANONE FiECVNDO
P ART.
i
gruui»
rmfecon*
Hypothe-
ius recluc
part.Angu
circuli xc.
Quadram
Bajis Hypotenujk
IOO, ooo
Perpendiculum
Hypotcmfa Perpendiculum
100,000 -
Bafis
congrua
Perpendiculo
PIJUPHEJLIA
ccmmo-
i
Triangvli Plani Pectangvli
SEV, AD TRIANGVLA.
Quadrans
circuli xc.
part.Angu
Iu, reflus,
Hypote-
nuix con-
gruus.
Circa-
commo-
Triangvli Plani R ectangvli
Hypotenufa
IOO, ooo
Perpendiculum Bafts
E CANONE Si-
nuum
l ls
IOO, OOO
P erpendisulum Hypotenufa
E CANONE FACVNDO
FtEcundiffimoquc
SEK1E
SE C EN D ^AC
Perpendiculum
IOO, ooo
Bajis Hypotenufa
E CANONE FA5CVNDO
Farcundiffimoque
TEK^TI J
lo ad-
daci
UJIST*
Bafi
coftgrua
i r
congrua
Baii
residva
■ dati
. Io ad«>
XXXI
XXXII
17
3 5, 0 48
i 7
35, 075
XXXIII
XXXIIII
><•■“
3 5, 1 3 0
XXXV
XXXVI
1 7
35,257
L- 7
3 5 , 184
XXXVII
XXXVIII
35.ai|
3 5, 2 3 9
XXXIX
XL
3 5 , 266
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5 5, 2 9 3
XLI
LXII
& 7
3 5, 3 2 o
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XLIII
XLIIII
XLV
XLVI
& 4
3 5, 375
1 7
3 5, 40 2
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XLV1I
XLVIII
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3 5,48^
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LII
LIII
LIIII
LV
LVI
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LVIII
LIX
LX
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b- b-
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3 5, 8 37
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283, 780
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37,^87
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37,720
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io< 7 , 8#5 9
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IO#, 877 6
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fi » 7
282,471
37,887
j »
37 , 920
c, . O
io 6, 93*
io#, 948 1
fi 5 fi
2«3, 714
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282, 254
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282, 037
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37 , 98 *
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281, 821
x 1 €
281, #05
1 1 f
281, 390
fi » r
281, 175
j f
3 S, 020
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io#, 983 6
11 5 3
io#, 99 5 5
2#3, 62 i
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2 #2, 791
3 8, 08#
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i T &
107,007 3
1 j 9
107, 019 2,
2 #2, 5#i
fi fi 9
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280, 9#o
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280, 74 #
3 8, 1 5 3
38, 18#
ll 3
10 7, 031 6
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280, 53 Z
2 80, 3 1 £T
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107, 054 8
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107, o## 7
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2 #1, #4#
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107, 0787
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107,090 <x
j, » 8
2 # I, 190
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2 #0, o# 3
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2 79 , * 7 ^
X I X
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260, 7 3 *
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XXX
nuum
E CANONE SI-
SE C EN D
SZS^If.
Eaicundifs imoque
E CANONE IACVNDO
TERJl^f
E CANONE F1CVND O
Bafts Perpendiculum
Bafts Hypotenufa,
Perpendiculum Hypotenufa
- 100 , ooo
IOO, ooo
100 , ooo
Hypotenufa,
Perpendiculum
Bafts
XXIX
XXVIII
XXVII
XXVI
XXV
XXIIII
XXIII
XXII
XXI
XX
XIX
XVIII
XVII
XVI
XV
XIIII
XIII
XII
XI
X
IX
VIII
VII
VI
V
IIII
III
II
S C R V F.
LX IX.
RlANGVLI LAN! ReCTANGVLi
PART.
congrua
Perpendiculo
PER.IPHER.IA
comrao-
Ciicu-
gruus.
nufx con*
Hypote-
lus reftus.
part.Angu
circuli xc.
Quadran*
Qaadraas .
circuli xc,
pare. Angu
uis re£his t
Hypo te-
nuia: con-
gruus.
Circii-
CANON aM JtCh E M ATI CVS,
: riangyli Plani Rectangyli
commo-
PSS.EPHE 1 LIA
Perpendiculo
congrua
Hypatm^s
IOO, ooo
Perpendiculum Bafs
Bajis |
IOO, OOO
Perpendiculum Hypotenufa
Perpendiculum
IOO, ooo
Bafis Hypotenufa
!oad=»
dati
SLESI 0 VA
Bafi
congrua
PART.
xxi.
iSCEVP.
E CANONE SI-
nuum
j
E CANONE F 1 CVNDO
F secundi, fsimoque
3 E e
, SECrN D.yf
E CANONE F 1 CVNDO
Fsecundifsimoque
TE ATI, A
♦ |
3 5 » 8 3 7
93 > 358 0 j
3 8, 3 86 , 107, 1 14 5- |
| 26o, 509
2 ? 9 , 043
LX
I
II
35, 864
% y
35, 891
i @ 4,
93 , 347 6
j a 4,
93,3 37 2.
i 7
3 8, 420
3 8,45 3
1 t e
107, 1265
1 i 9
107, 1384'
% t,
16 Q> 28?
% i
260, 057
2- 11 l
278, 8 3 2
III
278, 62 I
LIX
LVIII
III
IUI
35, 918
1 7
3 5 , 9 49
1 0 f
9 3 , 3 7
■104,
93 , 3 16 3
i +
38,487
_ * 1
3 8, 520
S i 0
107, 1504
1 i e
107, 162 4
i i «5
£59,831
i » f
259, 606
.ili
278, 410
% £ @
278, 200
LVII
LVI
V
VI
A &
3 %, 973
t 7
3 6, ooo
r 0 5
93, 305 8
. 104,
9 3 U 9 5 4
38 , 55 3
38, 587
lio
107, I74 4
1 1 S
107, 186 $
& 1 £
259,381
i i y
2 5 9, I 56
3 , S O
£ 77 , 990
aio
277, 780
LV
I UTI
VII
VIII
.1 7
3,6,027
s. 7
$6,0 5 4
1 0 ?
9 3 > 2-^4 p
1 s y
93, z74 4
i s
38,620
3 8, 654
107, 198 5
1 1 0
107, 2 10 ?
2 5 8, 9 3 2
1 i 4
2 5 8, 708
i 0 i>
277 , 5 71
i 0 9
277, 362
LXII
LIX
IX
X
y 7
3 6, 081
i 7 ,
3 6, 108
10 £
93,163 p
Io £
93 > 2-5 3 4
3 8, 687
„ 5 +
3 8, 721
i i i
107, 11 Z 6
1 & 1
107, ^34 7
i 1 4.
2 5 8,484
*■ * *
258. 26!
i 0 9
277, 15 3
i 0 *#
2r (2 y 4 1
LX
L
XI
XII
a. 7
3 6, 1 3 5
*■ 7
36, 162
1 0 y
9 3, 241 $
i 0 <5
93, 232 3
„ i i
38 , 754
3 8, 787
ii s
107,246 8
ii %
107, 2 5 8 s>
i * t
2 5 8, 03 8
i ?. $
257, 815
a! 0 ?
276, 737
* - & e 7
276, 530
XLIX
X LVIII
XIII
XIIXI
s &
36, 190
36, i 17
IO £
9 3, ui 8
io *$
9 3, XI I X
3 8, 82 i
38, 854
1 t ?
107,271 O
1 i I
107, 283 1
i i i
2 5 7 > 5 9 3
i 2 2
257, 371
276, 323
i © T
276, 1 16
XLVII
XLVI
XV '
XVI
36,244
36 , 171
1 0 s
93, zod 7
1 e S
93 , * 9 ° 1
38, 888
_ H
38 , 921
it 1
107, 295 i
» » *
107, 307 4
i i i
257, 149
i i 1
2 5 6, 92 8
i e 7
275, 909
1 0 ®
275, 703
XLV
XLIIII
XVII
XVIII
* 7
36, 298
3 6, 3 £ 5
J 0 r
93, 179 <?
1 0 6
93, I69 O
38, 95 5
38,9^8
107, 319 5
107, 331 7
i i 4
256, 707
iie
256,487
a 0 «r
275>497
i 0 £
2 75, 292
XLIII
XLII
XIX
XX
1 7
3^, 352
1 7
36,379
i O «
93,158 4
io e»
9 3 , 147 8
5 *
3 9, 022
? j
3 9 , 055
107, 343 8
i -i s
107, 3560
ile
256, 267
i i 0
256, 047
1 0 £
275, 087
i 3 f
274, 88 2
XLI
XL
XXI
XXII
» 7
• 36, 406
i 7
36,453
£ O £
9 3,137 3
Id £
93,126 8
A*
39,089
s i
39, 122
1 1 1
107, 368 2
ti j
107, 380 5
255, 827
% 1 5*
255, 608
1° f
274, 677
i 0 4
2 74, 47 5
XXXIX
XXXVII]
XXIII
XXIIII
i »
3 6, 46 1
36,488
£ O &
93,116 z
Io
93 U 05 6
* +
3 . 9 , i ? <7
* +
3 9 , 190
107, 392 7
I % %
107,404 9
1 r 9
25 5 , 389
i i S
255 , 170
2. @ 4»
274, 269
S 04
274, 065
XXXVII
XXXVI
XXV
XXVI
36, 515
i 7
3 6, 542
lo <5
93,095 0
j 0 7
93,084 3
39, 223
» 4
3 9 , 2 57
1 1 %
107,417 z
J i *
107,429 5
t l &
254 , 95 2
i I S
254,734
i @ 5
Z73, 862
% @ |
273,659
XXXV
XXXIIII
XXVII
XXVIII
3 6, 5 69
3 6, 5 96
2 0 (S
93,073 7
s 0 if
93,063 I
39 , 290
i +
3 9 , 3 24
107,441 7
1 & j
107,454 0
i 4 S
254, 516
i 5 7
2 54 , 2 99
i e 5
273,456
i 0 %
273, 254
XXXIII
XXXII
XXIX
XXX
i 7
3 6,62 3
1 7
3 6, 6 5 0
.* 3 7
93,052 4
10 *
93,041 8
3 9 , 357
1 4
39 , 39 i
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107, 466 3
107,478 h
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2 54 , 0S2
l » 7
253, 865
i 0 i
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1 0 1
272, 850
XXXI
XXX
j
SECFND^A
mium
E CANONE SI-
3 E 11/ E
Fxeundifsimoque
E CANONE F1CVNDO
congrua
Baft
Bdfs Perpendiculum
Bafis Hypotenufa
SL S S I D V A
IOO, ooo
IOO, ooo
dati
Hypotemfa
Perpendiculum
TEATIS
Fxcundifsimoque
SCXVI,
LXVIII.
E CANONE F1CVNDO
Perpendiculum Hypotenufa
IOO, ooo
flS
P A r. T.
congrua
Perpendiculo
PiR. IMBRIA
<3
gruus.
nufe con*
Hypote-
lus refius.
psrt. Angu
circuli xc.
Triangyli p lani Rectangvli
COmmo» j Quadrans
Circo-
SEV, AT) TRIANGVLA, ,
TrianguI' Plani Rectangvlx
Cit &” — — Io ad-
Quadrans
circuli xe.
part. Angu
Ius rectus,
Kypote-
nufse con-
commo-
PERIPHERIA
Perpendiculo
congrua
Hypotenufa
IOO, ooo
Perpendiculum Bajis
Bajis
IOO, OOO
Perpendis ulum HjpotenuJk
•Pe^^bculum
IOO, ooo
Bafis Hypotenufa
io aa-
datl
RISIDVA
Bali
congrua
gjuut. |
PART
E CANONE SI-
E CANONE FAECVNDO
E CANONE F^CVNDO
XXL
nuurn
FaecundiiTimoque
Fiecundiffim 6 que
SE xj i
ScKVP.
- PKJM^f
S ECr ND y€
Triangvli Plani Rectangvli
I ■
II
III
IUI
V
VI
VII
VIII
IX
X
XI
XII
XIII
XIIII
XV
XVI
XVII
XVIII
XIX
XX
XXI
XXII
XXIII
XXIIII
XXV
XXVI
XXVII
XXVIII
XXIX
XXX
CQJlgliict
B.E S £ D V A
dati
lo ad»
CANON q^cathem aticvs.
Triangvli Plani R ectangyli
eirculi se.
Pare. Angu
Ius reiSus,
Hypoce-
nufar con-
gruus.
comma-
SSSUfHIUIA
Perpendiculo
congrua
Hypotemfa
IOO, ooo
Perpendiculum Bajis
Bafis
IOO, OOO
Perpendiculum Hypotenujk
Perpendiculum
IOO, ooo
Bafis Hypotenujk
Io ad- t
dati
RISIDVA.
Bafi
PART. |
E CANONE SI-
E CANONE F1CVNDO
E CANONE F1CVNDO
XXI L
ilUUffl
iarcundiisirnoque
SEHJ E
F*cundifsim6gue
1 ■
SCRVP.
j
S E C y N D jC
1 ff. |
3 7 » 4 * *
9*> 718 4
40,403
107,853 5
247 » 5 09
2 66, 947
37*485
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92,^07 5
IO <9
92, 696 d
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11 7
107,8 66 2
1 i 7
107,878 9
x @ 7
247, 302
107
247,095
246, 888
z 0 £
24*, * 82
' 19 %
266, 755
i 9 X
266, 563
1 9 1
2 6 6, 3 7 I
1 9 1
2 66, 180
37 » 54 *
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92, <5-85 7
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246, 0*5
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245,860
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245,655
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265, 799
265, 609
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265,419
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265, 229
1 S 9
265, 040
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264, 851
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264, 662
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107,955 3
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92,609 0
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40, 707
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108,006 5
1 0 4.
245*247
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245,043
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108,032 I
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244,839
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3 7» 865
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92 , 554 0
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92, 543 0
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40, 945
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108,057 8
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264, 097
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263, 909
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263,722
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92,498 9
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41, 047
14
41, 08l
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108,09* S
_ 119
108,109 4
Z 0 x
243,623
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243,421
187
263, 348
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16 1,6%
38, 016
38,053
92,487 8
1 r e
92 , 47<7 8 j
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4 T » 1 1 5
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41, 149
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108,122 3
1 j 0
108,135 3
i 0 1
243, 220
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243, 019
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262, 976
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262, 79O
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262, 604
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262, 4I9
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108,148 2
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242, 818
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242,618
38 »i 34
38,1*1:
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92,443 5
II U .
92,432 4
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41, 251
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108, 174 z.
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108,187 i
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242,418
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242, 218
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92,410 z
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108,213 2
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242, 018
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199
241, 620
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241,421
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261, 864
184.
261, 680
184.
261,496
1 8 5
261, 3 i 3
38, 241
38, 2*$
3 1 I
92 , 399 1
92,388 0
41, 3^7
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41,421
3 1 ©
108 , 226 ’ Z
0 1 J a
I0 8, 2 3 9 2
LX
LIX
LV III
LVII
LVI
LV
LIIII
LIII
LII
LI
L
XLIX
XLVIII
XLVII
XLVI
XLV
XLIIII
XLIII
XLII
XLI
XL
XXXIX
XXXVIII
XXXVII
XXXVI
XXXV
XXXIIII
XXXIII
XXXII
XXXI
XXX
T M .yi
auum
E CANONE SX-
Bajis Perpendiculum
IOO, ooo
Hy potenti fu
S ECFN
se kjz
Fxcundifsimotjne
E CANONE FiECVNDO
Bajis Hypotenujk
IOO, ooo
Perpendiculum
TEKTl^t
Farcundifsimoque
E CANONE F JL C V N D O
Perpendiculum Hypotemfa
IOO, ooo
Bajis
Triangvli Plani Rectangvli
SCRVP.
LX V 1 1 .
PArT. ( S
_ J. | gruus.
uo'.-uia j mifse cc
ferpendicolo j j : Hypote-
PtRIPHEiUA ijjlus rc-ft,
j ] i pwt. An
1 1 ' circuli ■
comma- j j : Quadra
Circu- .<
SEV, AD TRlANGVLA.
Qtjadrans
circuli xc.
part.Angu
Ius rcflus
Hypothe-
nul.-E con-
gruus.
CtrcU"
XXX
XXXI
XXXII
XXXIII
XXXIII I
XXXV
XXXVI
XXXVII
XXXVIII
XXXIX
XL
XLI
XLII
XLIII
XLIIII
XLV
XLVI
XLVII
XLVIII
XLIX
L
LI
LII
LIII
LIIII
LV
LVI
LVII
LVIII
LIX
LX
1 congrua
Bafi
J SLSSIDVA
dati
lo ad-
T riangyli Plani Rectangvli
commo-
PERIPHERIA
Perpendiculo
congrua
Hypotenupi
IOO, 000
Perpendiculum Bafis
Bafis
IOO, OOO
Perpendiculum Hypotenujk
Perpendiculum
IOO, OOO
Bafis Hypotenupi
PART.
XXII.
E CANONES I-
nuum
E CANONE riCYNDO
Fsecandiffimoque
S,E J^l X
ECANONE fICYNDo
Fsecundiflimoque
SCJIYP,
TKJ
SE C yN D x.s€
TERJ 1 AC
lo ad-
dati
«.ist&Vi
Bafi
congriia.
F KJ M AC
mium
E CANONE S I-
Bafis Perpendiculum
IOO, ooo
Plypotenufx
3 8 > 2 95
1 7
38, 322
IX 2 j
92, 37* 3
IX I |
92, 3*5 7
1 7
38, 349
x 7
38, 3 7*
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92,354 5
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92, 343 4
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38,403
z 7
38,430
I X 2
92, 332 z
1 1 t
92, 3 2 1 0
% 6
38,45*
$8,483
XI I
92, 309 9
I I X
92, 298 7
1 7
3 8, 5 10
1 7
38, 5 37
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92, 27* 3
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92, 197 6
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38,832
38, 859
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92, 141 2,
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92, 129 9
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38, 939
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108, 383 4
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108,409 8
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108, 43 <5 x
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108, 449 5
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SECVNDAC
SEZJE
Farcundiftimoque
E CANONE FACVNDC)
Bajis Hypotenupi
IOO, 000
Perpendiculum
241,421 , 2*1, 3 I 3
X 9 *
241, 223
198
241, 025
184
2*1, 119
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240, 827
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260, 581
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240, 43 1
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240, 2 3 5
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240, 038
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239, 841
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196
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238, **8
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258, 9|°
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238, 279
179
258, 591
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2 5 8, 412
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238,085
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237, 891
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237, *97
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25 5, 930
XXX
XXIX
XXVIII
XXVII
XXVI
XXV
XXIIII
XXIII
XXII
XXI
XX
XIX
XVIII
XVII
XVI
XV
XIIII
XIII
XII
XI
X
IX
VIII
VII
VI
V
IIII
III
II
I
♦
T E RJT I vsC
Fsecundiflimoque
E canoNe FACVNDO
SCRVP,
LXVII.
PART.
Perpendiculum Hypotenupi
IOO, 000
Bajis
RlANGVLl L AN I ReCTANCVLI
congrua
Perpendiculo
PIIUPHIRIA
commo-
- Circu-
gruus.
nufae cob-
Hvpotht-
lus reftus
part.Angu
circuli xc.
Quadratu
Quadrans
circuli ttc.
part. Angu
li
Iu s reftus,
Hypote-
nufae con-
gruus.
Circu»
cqmtno-
PSKtTHS RIA
Pe rpcndiculo.
congrua
PART.
XXIII.
S C R V P.
I
II
III
IIII
V
YI
VII
VIII
IX
X
XI
XII
XIII
XIIII
XV
XVI
XVII
XVIII
XIX
XX
XXI
XXII
XXIII
xxim
XXV
XXVI
XXVII
XXVIII
XXIX
XXX
eongtuu
Baii
UilD V A
dati
lo ad»
CANON & 5 VC A THE M ATI C VS,
RlANGVLI '"LANI ReCTANGVLI
Hypotenujk
100 , ooo
Perpendiculum Bafis
E CANONE SI-
nuum
Bafis
IOO, ooo
Perpendiculum Hypotenujk
Perpendiculum
IOO, ooo
Bafis Hypotenujk
E CANONE FiECVNDO
Faccundifsimdque
se KJ'E
SECVHD^€
E CANONE T JE C VND 0
Fx 8 undifsim 6 g ue
j T E XT t kA
3 9 , 07 3
92, 050 5
42, 447
108,636' 0 j
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39,127
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190
2 3 5 > 395
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235, 2o<f
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92, 016 4
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92,005 0
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42,757
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108, 757 3
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188
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42, 929
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108, 82 5 i
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91, 867 6
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232, 7| 6
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91, 844 6
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43, 032
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108, 865 p
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108, 879 5
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232, 197
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252, 986
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231, 641
231,456
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2?0, 350
169
2 5 1, 2 8 8
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43,447
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43 , 48 l
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230, 167
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229, 984
IUS
250, 9^2
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nuum
CANONE 51-
B d fis Perpendiculum
IOO, ooo
Hypotenupi
SECVN Djt
stujz
Fajetindifsimoque
CANONE F1CVNDO
Bajis Hypotenujk
IOO, ooo
Perpendiculum
TEXTIS
Faecundifsimoque
Io ad-
daci
aisi » y a
Eafi
congrua
LX
LIX
LV III
LVII
LVI
LV
LIIII
LIII
LII
LI
L
XLIX
XLVIII
XLVII
XLVI
XLV
XLIIII
XLIII
XLII
XLI
XL
XXXIX
XXXVIII
XXXVII
XXXVI
XXXV
XXXIIII
XXXIII
XXXII
XXXI
XXX
SCRVP.
LXV I ,
E CANONE F 1 CVNDO
Perpendiculum Hypotenujk
IOO, ooo
Bafis
PArT.
congrua j
Perpendicul» j
PEJUPHERiA
Triangvli P LANI R ectangvli
commo-
Circu-
gruus.
nufe coipi
Hypote- -
lus re&usi
part. Angi ;
circuii jra
Quadranti
$EV, AT) TRIANGVLA . .
IANGVLI pLANI RECTANGVLI
Quiedrans
circuli xc.
part.Augu
Ius re&us,
Hypote-
nuix con-
commo -
PEMPHIRIA
Perpendiculo
congrua
Hypotenufa
IOO, OOO
Perpendiculum Bajis
Bajis
IOO, OOO
Perpendiculum Hypotenuja
Perpendiculum
IOO, OOO
Bajis Hypotenuja
gnui?.
pART.
E CANONE SI-
E CANONE FjECVNDO
E CANONE FJECVNDO
XXIII.
nuum
FaecundiiTirnoque
Fscundiffimoque
SEKJE
S C R V F.
SECF^D^f
TE^Tllyt
Io a ci-
dari
l'i S 1 D V A
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congrua
congrua
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St £ $ I © V A
dati
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nuum
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is
Perpendiculum
IOO, OOO
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SECFND^f
scrje,
Fscundifsimoquc
E CANONE I 1 CVNDO
Bajis Hypotenuja
IOO, OOO
Perpendiculum
TEXJl^f
Ejectandi (limo que
J) xxx
• 59,875
91, 70# 0 ,
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39, 928
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XXXIII
3 9,9 55
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XXVII
XXXIIII
39, 982
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XXVI
XXXV
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XXIIII
XXXVII
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40, 06 1
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249,45 0
XXII
XXXIX
40, 1 is
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XXI
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40, 142
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XVI
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2- 7
4 °> 275
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109, 252 4
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227,267
248, 29 1"
XV
XLVI
3 . 6
40, 3 01
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91, 519 4
44, o i 6
109, 26 d 4
2 27, 6 § $
248, i 3 i
XIIII
XLVII
40, 3 2 8
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91,507 7
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44, 070
109, 286 4
1 7 9
2 26,90 9
247,
XIII
XLVIII
40,3 55
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40,514
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LXVL
E CANONE FAECVNDG
Perpendiculum Hypotenuja
IOO, OOO
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PART.
T Riangvli Plani |ectangvli
congrua
Perpendiculo
PER.iPHJtS.IA
commo-
Ck CU-
grUiu.
nufs: con-
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part.Angu
circuli xc,
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coramo-
«irculi xc.
part. Angu
Ius redtus.
JHR.IPHI1UA
Mypote-
Pe rpendiculo
nufce con-
congrua
gtuus.
P A R T.
XXIIII
J
senp.
II
f
III
IIII
¥
VI
VII
VIII
IX
X
XI
XII
XIII
X.IIII
XV
XVI
XVII
XVIII
XIX
XX
XXI
XXII
XXIII
XXIIII
XXV
XXVI
XXVII
XXVIII
XXIX
XXX
congrua
Ba(i
JLI S I O Y A
dati
Io ad-
CANON ca tATHEMATICVS ,
R I A N G Y L I 1 ’lASI B. BCTAKGUI
Hypotenufe
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Perpendiculum Bajis
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nuum
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nr-
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91,008 i
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Bajis
100, ooo
Perpendiculum Hypotenufe
Perpendiculum
IOO, ooo
Bajis Hypotenufe
E CANONE F^CVNDO
Fatcuadifsimdque
SSRJE
S E c y N D ,A
E CANONE FjECVNDO
Jtsecundifsimogue
TETxTl^t j
lo ad-
daci
&ISIDYA
Bafi
congrua
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109,463 d
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2 24, g 04 j 245, 859
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244, 900
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244, 74 1
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244,423
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244, 264
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244, 106
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243, 948
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243, 005
242 , 848
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242,692
242, 536
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242 , 225
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241, 760
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241, 609
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241, 296
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LVII
LVI
LV
LIIII
LIII
LII
LI
L
XLIX
XLVIII
XLVII
XLVI
XLV
XLIIII
XXXIX
XXXVIIJ
XLIII
XLII
XLI
XL
XXXVII
XXXVI
XXXV
XXXIIII
XXXIII
XXXII
XXXI
XXX
nuura
E CANONE SI-
Bdjis Perpendiculum
100, 000
Hypotenufe
SECyND^€
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TEEJIAP
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LXV.
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SEV, AD TRIANG^TLA.
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Quadrans
circuli xc.
part.Angu
5us re&us,
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commo-
PERIPHERIA
Perpendiculo
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Hypotenufa
IOO, ooo
Perpendiculum Bajis
Bafis
10 0,00 0
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IOO, ooo
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dati
R E 5 1 D V A
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gruur.
PART.
E CANONE SI-
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! 4 *> 4^9
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109,894 8
2 19,430 ] 24 r,I 42 !J> XXX
XXXI
XXXII
l 7
4 1 » 49 6
1 6
41, 512
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90, 984 1
11 I
90, 972 0
45, 608
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109, 9 24 0
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219, 2 6 l
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240, 988
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XXIX
XXVIII
XXXIII
XXXIIII
1 7
41, 54 9
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109,938 d
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109,953 *
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2 1 8, 92 3
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218,755
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240, p8 1
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240, 5 28
XXVII
XXVI
XXXV
XXXVI
1 7
41,602
L 6
41, 6 Z§
11 2
90,935 7
11 l
90,923 d
J V
45, 748'
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45 , 784
l 4. 6
109, 967 8
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109,982 5
I 6 8
2 I 8, 787
16 8
2 1 8, 419
J S 3
240, 375
1 S 3
240, 2 2 2
XXV
XXIIII
XXXVII
XXXVIII
41^5 5
1 6
41, 6 Si
11 1
90,911 5
XI 1
90,899 4
5 s
45 , 819
3 *
45 , 854
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1 1 0, 0 1 1 8
2 18,251
I 6 7
2 I 8, 084
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240, 070
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2 3 9, 9 1 8
XXIII
XXII
XXXIX
XL
i 6
4 1 >797
4 i >734
90,887 3
11 1
90,875 1
45, 889
3 >■
45 , 924
1 T 7
1 1 0, O 2 6 5
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110,041 z
16 8
217, 916
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217, 749
1 4 1
239, 7 66
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239, 614
XXI
XX
XLI
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1 6
4 1 , 760
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41, 787
21 i
90,863 0
11 2.
90, 8 5 0 8
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45, 960
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45 , 995
1 + 7
110,05 5 P
* 4 - 7
110,070 6
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217,582
16 6
217,416
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2 39, 462
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239, 3 II
XIX
XVIII
XLIII
XLIIII
% 6
4 1 »
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41, 840
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90,838 7
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46, 030
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46, 065
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217 , 249
16 6
2 17, OS?
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239, I59
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XVII
XVI
XLV
XLVI
41, 866
i 6
41» g 92
SI 1
90,814 3
XI 1
90,802 I
5 <5
46, Ioi
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46, 1 3 6
1 4 - 7
110,114 8
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110,129 6
16 6
216, 917
166
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238, 857
1 4 0
238, 707
XV
XIIXI
XLVII
XLVIII
a. 7
919
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41, 945:
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90,790 0
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90,777 S
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2 3 8, 556
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238, 406
XIII
XII
XLIX
L
1 7
4 1 » 97 ^
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41, 998
11 i.
90,765 d
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90,753 3
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46, 242
3 V
46, 277
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110,174 0
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42, 077
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46, 383
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46,418
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110,233 4
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110,248 3
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2 15, 596
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215, 104
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42, j 8 3
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1 7
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213, 154
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XII
42, 578
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42, 788
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42,815
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42, 841
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100,000
Bafis
lo ad-
dati
USIDYA
Bafi
congrua
xxx
XXIX
XXVIII
XXVII
XXVI
XXV
XXIIII
XXIII
XXII
XV
XIII
XII
XI
X
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VIII
VII
VI
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III
II
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TRiANGVLI pLANl RECTANGVLI
congrua
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PEE.1PHEE.IA
commo-
Circu-
gruru.
nufre con-
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lus re£tm.
part.Angu
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nuis con-
gius,
congrua
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dati
lo ad-
CANON c^f ATHEM ATICVS,
TriANGYLI Phani Rectangyli
commo»
PIB.tFHEB.IA
Perpendiculo
congrua
Hypotenujk
IOO, ooo
Perpendiculum Bajis
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IOO, ooo
Perpendiculum Hypotenujk
Perpendiculum
IOO, OOO
Bafs Hypotenujk
ioad-
dati
S.ESIDYA
Bafi
congrua
PAR.T.
XXVI
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nuum
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Fxcundifs if&dau c
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TEFJl
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Perpendiculum Hypotenujk
1.0 pj ooo
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♦ i
41 , 837
89, 879 4
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m, 260
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204, 125
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LIIII
VII
VIII
1 d
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nufx con-
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100, 000
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XXIX
XXVIII
XXVII
XXVI
XXV
XXIIII
XXIII
XXII
XXI
XX
XIX
XVIII
XVII
XVI
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XIIII
XIII
XII
XI
X
IX
VIII
VII
VI
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III
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♦
S C R V F,
Lxnr.
PART.
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congrua
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PBRlPHItlUA
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gruus.
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part.Anga
circuli xc.
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part. Angu
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fruus.
comino-
PIRIPHIB.IA
perpendiculo
congrua
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PART.
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XXVII
0
nuam.
S C R. V P,
I
II
III
IIII
V
VI
VII
VIII
IX
X
XI
XII
XIII
XIIII
XV
XVI
XVII
XVIII
XIX
XX
XXI
XXII
XXIII
XXIIII
XXV
XXVI
XXVII
XXVIII
XXIX
XXX
PJ \J M
PUTI
nuum
1 CANONE SI-
congrua
Baii
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R .5 S I D V A
IOO, OOO
dati
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100,000
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ioo, ood
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SEC r ND
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dati
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I
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V
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XV
XVI
XVII
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XIX
XX
XXI
XXII
XXIII
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XXV
XXVI
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CANON qMATHEMATICVS,
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XXIX
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XXXI
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LVI
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R.JS1DVA
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congrua
XXX
XXXI
XXXII
'XXXIII
XXXIIII
XXXV
XXXVI
XXXVII
I
Ixxxviii
XXXIX
XL
XLI
XLII
XLIII
XLIIII
XLV
XLVI
XLVII
XLVIII
XLIX
L
LI
LII
LIII
LIIII
LV
LVI
LVII
LVIII
LIX
LX
congrua
Bali
StSiOVi
dati
io ad-
5 2 > 250
8 5, 2*4 0
2- f
5*> 275
1 . 4 »
52, 299
1 y r
85, 248 8
„ 1 S i
85,233 *
52, 324
52, 349
1 A 1
8 5,218 4
_ 1 y 1
85,203 Z
52, 374
2- s
52 , 399
n * T J
85, 187 9
1 f *•
85,172 7
1 4
52,423
1 s
5 2, 448
- 1 * *■
85, 157 5
- 1 1 5
85, 142 1
5 2, 4* 3
52,498
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85,12 * 9
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85, III 7
x 4
5 2, 5 2 2
52 , 547
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8 5,09* 4
1 y »
85,081 1
5 2 , 5 72
52, 597
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85,0*5 8
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85,050 5
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52, 720
52, 745
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84, 973 9
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84, 958 6
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5 £5 794
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84,943 3
1 y 4
84,927 P
5*> 819
1 y
52, 844
_ 1 5 5
84, 912 6
„ „ 1 y y
84, 897 3
5 2, 8*9
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84, 881 1
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84, 866 4
5 2, 9 1 8
52, 943
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84,851 O
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84, 835 6
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5 2, 9*7
52, 992
84? 820 z
1 y 4
84, 8 04 8 1
nuum
E CANONE SI-
Bafis Perpendiculum
I oo, ooo
Hypotenufa
XXX
XXIX
xxvm
XXVII
XXVI
XXV
XXIIII
XXIII
XXII
XV
XIIII
XIII
XII
XI
x
IX
VIII
VII
VI
V
IIII
III
II
I
♦ ■
S C RVt,
LVIII
PART.
Triangvli Plani Rectangvli
congrua
Perpendiculo
PBRIPHERIA
commo-
Citcu-
gruus .
nulas con-
Hypote-
lus reftus.
part. Angu
circuli xc.
Quadrans
I
CANON zMATHEMATICFS,
RlANGVLl LANI ReCTANGVLI
Circu-
Qgadrans
circuli xc.
part. Aagu
lu s re&us.
toisrao-
Hypotenujk
Bajis
Perpendiculum
io aa-
dati
FXRI9HZ1UA
IOO, ooo
200,000
IOO, ooo
K E SI © TA
Bafi
congrua
Hypoce-
nufe con-
perpendicula
congrua
Perpendiculum Bajis
Perpendiculum Hypotenujk
Bajis Hypotenujk
gruus.
PART.
E CANONE SI-
E CANONE F1CVNDO
Eaeeiindifsimdcjue
sr,p^iE
E CANONE F1CVNDO
Ejeoundifsimoguc
XXXII.
SCRff.
1 p%rM',A?
SEC VND
TE^TH-f
♦ i
5 2 » 99 2
84,804 8 |
^2,487
11 7, 917 8
i< 5 o, 033
188, 708
| LX
i
ii
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5 3 » oi 7
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5 3 » 041
7 y +
84, 789 4
1 y 4
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4, 0
< 52 , 527
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1 1 7 » 9 3 9 *
1 1 y
117, 9<5o 7
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159, 827
8 8
188, <520
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188, 533
LIX
LV III
iii
mi
1 y
5
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5 3 » 091
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84, 743 1
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LVII
LVI
V
VI
53 » 115
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84,712 z
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62, 73O
5 fT — 3 “
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188, 270
8 7
l8 8, I83
LV
LIIII
VII
VIII
z 4-
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53,189
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84, 696 7
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84,681 3
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15 9 » 3 11
105
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1 8 8, 09 5
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l8 8, OOS
LIII
LII
IX
X
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53,414
53 » 2 3&
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11 8, 111 5
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Il8, I33 O
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159, 105
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I87, 92 1
8 7
187, 8 34
LI
L
XI
XII
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53,2^3
53,288
84,43^. 8
84» 619 3
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118, 154 <5
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1 5 8, 900
1 0 }
15 8, 797
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187,747
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I 87, < 5 < 5 l
XLIX
XLVIII
XIII
XIIII
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5 3 » 3 1 2
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8 4, 6 0 3 8
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11 8, 198 0
i 1 7
118, 2197
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158, <595
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158, 593
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187, 574
187, 488
XLVII
XLVI
XV
XVI
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53 » 3*i
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53 » 3 ^< 5 "
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84, 572 8
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84» 5 57 3
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117
1 18, 241 4
z 1 7
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158, 490
, 158, 388
8 7
187,401
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187, 3 15
XLV
XLIIII
XVII
XVIII
J* x y
53,411
1 4
5 3 » 43 $
1 y 6
84, 54I 7
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8 4, 5 2 6 z
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63,2 17
118, 284 8
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118, 306 5
1 0 Z
158, 28 <5
I 0 X
1 5 8, 1 84
I 87, 228
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I87, 142
XLIII
XLII
XIX
1
XX
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53,4^0
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84, 510 d
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84,495 x
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XLI
XL
XXI
XXII
53 » 509
53 » <34
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84,4^4 0
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1 1 8
118, 393 7
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157, 879
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XXXIX
XXXVIIJ
XXIII
XXIIII
1 +
5 3 » 5 5 ®
5?.?83
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84» 448 4
1 y 6
84,432 8
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118,415 5
119
118,437 4
I O Z
157, < 57<5
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15 7 » 5 75
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186,712
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I 8 6, 6 2 7
XXXVII
XXXVI
XXV
XXVI
5 3.^7
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84,417 ^
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84,401 6
4 1
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186,457
XXXV
XXXIIII
XXVII
XXVIII
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11 8 , 525 0
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XXXIII
XXXII
XXIX
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dati
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ffruus.
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E CANONE FACVNDO
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I
j XXXI
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I XXXII
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XXXIIII,
XXXV
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XXXIX
XL
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XLIIII
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XLVI
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XLVIII
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L
LI
LII
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LV
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LVIII
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53.750
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185,608
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100
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118,833 9
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XIX
XVIII
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54. 049
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184, 1 86
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VII
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83,882 9
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PER.iPUiR.lA
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Hypote-
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grum.
I
II
III
IIII
V
VI
VII
VIII
IX
X
XI
XII
XIII
XIIII
XV
XVI
XVII
XVIII
XIX
XX
XXI
XXII
XXIII
XXIIII
XXV
XXVI
XXVII
XXVIII
XXIX
XXX
congrua
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100, 000
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| PART.
XXXIlI
s e s. v p.
9
E CANONE Si-
nuum
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IOO, OOO
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Bafis
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LX
LIX
LV III
LVII
LVI
LV
LUXI
LIII
LII
LI
L
XLIX
XLVIII
XLVII
XLVI
XLV
XLIIII
XXXIX
XXXVIII
XLIII
XLII
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XXXVI
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XXXIIII
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IOO, OOO
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Hypotenuja
Perpendiculum
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comhio-
PER.IPHER.IA
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PART.
XXXV
SCUVP.
XXX
XXXI
xxxir
XXXIII
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XXXVI
XXXVII
XXXVIII
XXXIX
XL
XLI
XLII
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XLIX
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LI
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XXIX
XXVIII
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XXIIXI
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XXI
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XVII
XVI
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XIIII
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XII
XI
X
IX
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VII
VI
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LVIIX
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IIII
5 8, 849
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LIIII
VII
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169, 655
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169, 5 87
LIII
MI
IX
X
XI
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58, 990
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XLIX
XLVIII
XIII
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59, 084
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XLV 1 I
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59. 13 1
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XLIIII
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59, 178
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XLIII
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59,225
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XXXVIII
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59 , 3 *^
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XXXVII
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59 , 389
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XXXV
XXXIIII
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59,412
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80,437 6
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59,45 9
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100,000
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XXX
XXIX
XXVIII
XXVII
XXVI
XXV
XXIIII
XXIII
XXII
XXI
XX
XIX
XVIII
XVII
XVI
XV
XIIII
XIII
XII
XI
X
IX
VIII
VII
VI
V
IIII
III
II
I
❖
Faicundiffimoque
E CANONE FrECVNDO
Hypotenufa Perpendiculum
100, 000
Bajis
SCRV 1 >.
Liir.
PART,
T Riangvli Plani Rectangvli
congrua
Perpendiculo
per.iphejua
comrao-
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gruus.
mi fa; con-
Hypoche-
lus refttii
part.Angu
circuli xc.
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CANON oMATHEMATICFS,
Tjriangvli Plani R ectangvi.i
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circuli xc •
part.Angu
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Hypothe-
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PEXUffHlJUA
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t»
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IOO, ooo
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Bafis
IOO, ooo
Perpendiculum Hypotenufa
Perpendiculum
IOO, ooo
Bafis Hypotenufa
dati
R.ISIDYA
Bafi
congrua.
gruus. j
PA RX.
£ CANONES I-
E CANONE F1CVNDO
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XXXVII
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S C RV P*
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I
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166, 036
LIX
LVIII
III
IIII
60» 25 1
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60, 274
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165, 908
LVII
LVI
V
VI
1 4
60, 298
1 3
60, 321
176
79 > 775 P
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LV
LTITI
VII
VIII
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60, 344
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60, 3 £7
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79,740 8
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132, 144
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13 2, O64
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I65, 716
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165,653
LIII
LII
IX
X
‘ *
60, 390
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LI
L
XI
XII
60,437
3
60, 460
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79,670 6
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‘77
125,544 <r
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165,462
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165,399
XLIX
XLVIII
XIII
XIIII
‘ t
60, 48 3
1 3
6 0, $06
r 7 «5
79,63$ 4
1 7 s
79, 617 8
75 , 95 o
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75 , 99 *
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125,600 I
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XLVII
XLVI
XV
XVI
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79, 600 z
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76,042
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125,655 6
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131, 507
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XLV
X LII II
XVII
XVIII
t 3
60, $76
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79 » 547 4
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125,683 4
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125,711 3
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131, 269
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I65, 083
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XLIII
XLII
XIX
XX
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50 , 62 2
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60, #45
1 7 7
79 » 5*9 7
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76, 2 26
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125,739 i
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131, iio
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I64, 8 94
XLI
XL
XXI
XXII
60 , 668
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60, 691
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79,494 4
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79,476 8
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XXXIX
XXXVIII
XXIII
XXIIII
1 3
60, 714
1
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1 7 7
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130, 873
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XXXVII
XXXVI
XXV
XXVI
£0, 761
60, 784
79 » 4 2 3 8
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XXXV
x xxiiii
XXVII
XXVIII
1 3
6 0, 807
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177
79, 3884
177
79 » 370 7
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XXXIII
XXXII
XXIX
XXX
‘ 3 i
60, 8 5 3
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7 9
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164, 268 :!
XXXI
XXX
congrua
Bafi
USSIDTA
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PART.
gruus.
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Bafs Perpendiculum
100, ooo
Hypotenufa
Bafis Hypotenufa
IOO, ooo
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Perpendiculum Hypotenufa
IOO, ooo
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PEJUPHERIA
commo-
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XXX
XXXI
XXXII
XXXIIJ
XXXIIII
XXXV
XXXVI
XXXVII
XXXVIII
XXXIX
XL
XLI
XLII
XLIII
XLIIII
XLV
XLVI
XLVII
XLVIII
XLIX
L
LI
LII
LIII
Lltll
LV
LVI
LV II
LVIII
LIX
LX
1 riangvli Plani Rbctangvli
congrua
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dari
load-
conuno-
PlRIPHIlUA
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congrua
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IOO, 000
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dati
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1 P A R T.
XXXVii
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6 o, 876
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tRJ MJC
nuum
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IOO, 000
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TERJl^Z
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XXIX
XXVIII
XXVII
XXVI
XXV
XXIIII
XXIII
XXII
XXI
XX
XIX
XVIII
XVII
XVI
XV
XIIH
XIII
XII
XI
X
IX
VIII
VII
VI
V
IIIX
III
II
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fis
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PA R.T.
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Faecundiflimoque
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61, 589
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1(5 3, 3 <56
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III
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61,65$
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1 S 0
78,747 3
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78, 2(59
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127, 5 35
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LIXII
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VIII
1 i
61, 726
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XLIX
XLVIII
XIII
XIIII
6l, 864
6l, 887
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78, 5 <57 7
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78, 549 7
78 , 739
78,786
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78, 513 7
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126, 849
12(5, 774
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XLIIII
XVII
XVIII
< 51,9 H
61, 97$
i S 0
78,495 7
_ r S 1
78,477 (T
78, 92$
7 8, 97 5
1 9 j
ii 7,395 7
x 9 x
127,424 p
I 2 ( 5 , <598
7 fi
I 2 ( 5 , <5 2 2
fi Q~
I6l, 4O7
161, 34-i
XLIII
XLll
XIX
XX
, 1 *
6 2,001
. 4 *
^2, 024
1 8 0
78,459 *
1 8 0
78,441 d
4- 7
79 , 022
4. 8
79 , 070
1 9 j
127,454 i
X 9 X
127,483 4
7 fi
12 ( 5 , 54<5
, ^ 7 *
12 6, 471
l( 5 i, 188
f 9
I < 5 l, 229
XLI
XL
XXI
XXII
"ITT
<5 2, 04 <?
#2, o #9
_ 1X1
78,423 5
78,405 4
4 7“
79 , 117
47
79 , i *4
*■ 9 1
ii 7 > 5 ii 7
194
Ii 7 > 54 i 1
y 6
126, 395
12 6, 3 19
6 ©
I< 5 i t 149
_ * s»
I < 5 i, 110
XXXIX
XXXVIII
XXIII
XXIIII
i a
< 52 , 092
- * *
< 52 , 1 1 5
78, 3 $7 4
_ x 8 I
78,669 3
4 »
79 , ili
4 7
79, 25 9
X 9 4
1 1 7 , 5 71 5
X 9 4
127,(500 9
, 7 f
12 6, 244
12 ( 5 , 169
_ r 9
I( 5 l, 05 1
1*0, 992
XXXVII
XXXVI
XXV
XXVI
< 52 , 15^
i le
<59, l< 5 o
18 0
78 , 351 3
x 8 1
78 , 3 3 3 z
* J
79 , 3 0*
4 8
79 , 3 54
19 +
12 7 , <53 0 3
127,659 $
, 79
126, 09 3
126, oii
■ ■■ r
f 9 i
1*0, 93 3
1*0, 874
XXXV
XXXIII I
xxvii
XXVIII
x J
^2, 185
^2, 20 6
1 8 1
78,315 x
„ I 8 I
78, 2 97 O
4 7
79,401
4 8
7 9,449
X 9 f j
117,689 3
127, 71 i 1
7 f
125, 943
125, 8^7
i< 5 o, 815
f 9
i< 5 o, 75<5
XXXIII
XXXII
XXIX
XXX
C i
<52 , 229
<52, 251
I S I
78, 278 j9
x 8
78, 2<5o 8
4 7
79,49*
79 , 544
ii 7, 748 |
x 9 er
ii 7 , 777 P
7 y
125, 792
.7 ?
125, 717
I < 5 0, 698
160, 659
•XXXI
XXX
p^r r
Huum
E CANONE SI-
sEcrND^e
s e nat.
Faecundiffimocjue
E CANONE I 1 CVNDO
TEETl
Faecundiffi
ECAN ONE
SCRYP,
LI.
moquc
F 1 CVND O
PART.
congrua
Bafi
RSSIDVA
:t-Hi
Lft iid-
Bafis Perpendiculum
IOO, OOO
Hypotenufa
Bafis Hypotenufa
IOO, ooo
Perpendiculum
Perpendiculum Hypotenufa
IOO, ooo
Bafis
congrua
Perpendiculo
FEJUPHEfUA
comrno-
gruus.
nufe con- •
Hypothe- •
lus redus t
patt.Angu y
circulixc.
Q,uadrant s
Triangvli Plani Rectangvli
SEF, AD TR IANGFLA.
Truhgyii Plani r.ectangvli
i
Quadrans
circuli xc.
pari.Angu
lus re£tus ,
Hypo te-
nuia: con-
gruus.
Circii»
commo-
rER.IPHSB.IA
Perpendiculo
congrua
PAR.T.
'et
IOO, OQO
Perpendiculum Bajis
XXXVIil.
SCEYP.
xxx
XXXI
XXXII
XXXIII
XXXIIII
XXXV
XXXVI
XXXVII
XXXVIil
XXXIX
XL
XLI
XLII
XLIII
XLIIII
XLV
XLVI
XLVII
XL VIII
XLIX
L
LI
LII
LIII
LIIII
LV
LVI
LVII
LVIII
LIX
IX
E CANONE SI-
nuum
62,251
* i
62, 274
t
6 2, 2~9 7
* ?
6 2, 520
1 i
6 2, % 4 3
4 5
6 2, 366
i x
6 2 ,
1 i
62, 41 1
x 1
62, 45 3
x i
6 z, 45 6
» s
62, 479
x f
62 , 502
1 X
62,5 24
t : 5
«*, 547
62, 570
i x
62, 592
x ?
62 , 615
i 3
<$■2, 638
X %
62 , 660
62, 683
, * i
62, 70 6
62, 728
i *
**, 751
62, 774
r t
62, 796
6 2, 819
62, 84.2'
62,8 64
62, 887
6 2, 969
, i- *
6 2,9 3 2
78, 260 8
s x I
78, 242 7
I 8
78 , 2 24 6
18 x
78 , 206 ' $
1 8 1
78 ,l 8 8 3
1 8 1
78,170 2
.181
78, 1 5 Z I
i 8 x
78,133 9
18 1
78,115 7
18 I
78,097 6
18 1
78,079 4
1 8 X
7 8 , 06 l 2
s 8 x
78,043 O
I 8 I
78,024 9
18 X
78 , 006 7
«8 X
77,98 8 *
. 1 8 J
77,970 2
t 8 x
77,952 O
18 x
77, 9 3 3 81
1 S x
77,915 6
_ * 8 *
77, #97 3
* s i
77,879 1
77, 860 &
18 X
77,842 6
i 8 J
77,8*4 3
18 X
77,806 I
77,787 ^
4 s *
77,769 5
x 8 J
77,751 2
J 8 i
77,73* i>
77,714 £
Bajis
Perpendiculum j
IOO, OOO
IOO, OOO I
Perpendiculum Hypotenuf
Bafis Hypotenufet
t CANONE FAE CVNDO
E CANONE JICVNDO
Fascuiidilsimd que
Farcundifamoque
s e rje
SE C F N D yy€
TEATIS j
Io ad
dati
X H S I D V A
Bafi
congrua
7 9 , 544
1*7,777 ^
! 125,717
160, 63 9
XXX
79 , 5 9 1
4. 8
79 , 63 Q
0 1 9 6
127, 807 5
X 9 6
127 , 837 I
12 5, 642
125, 567
1 6 0, 5 8 0
160, 5.2 i
XXIX
XXVIII
79, 6§6
1 9
127, 8^6” 7
125,492
160, 4^*
XXVII
7 9 , 7 34
127, 89^ 4
125 , 417
f 8
I 6 O, 404
XXVI
79 , 7 $*
79, 829
x O S
127, 926 0
i !» 7
12 7,95 5 7
'7 4
125, 343
125, 268
X O 3 ^ ^ ^
I60, 287
XXV
XXIII I
79, 877
127,985 4
1*5, 193
, ■f^T
I60, 2 29
XXIII
• 4 * 7
79, 924
19 8
12 8,015 2
7 4
125, 119
r r 8
160 , I7I
XXII
4
79 , 97 *
8 o, 0 2 0
O 4 9 8
128,045 O
_ x 9 8
128, 074 8
125, 044
1 24, 969
<r 9
160,112
I60, 054
XXI
XX
80, o1>7
80, 115
_ 19 3
12 8, 104 6
128,134 5
124, 895
124, 826
5 T j?
159, 996
159 , 938
XIX
XVIII
80, 163
128, 1^4 3
124, 746
159, 880
XVII
80, 211
128,1194 2
124, 67 i
159, 822
XVI
80, 2 5 §
O ? O 0
128,224 2
1*4, 597
15 9 , 7*54
XV
80, 306
128,2 54 1
1 24, 5 * 3
159, 70 6
XIIII
0 + 8
80, 3 54
128,284 x
124, 449
1 5 9 , 648
XIII
4. S"
80, 402
_ i 0 a
128, 3 14 1
124, 375
159, 590
XII
80, 450
I 2 8, 3 44 I
124, 301
1 5 9 , 5 3 , *
XI
80, 498
n J 0 0
12 8,374 I
124, 227
1 5 9, 47 f
X
80, 546
80,5 94
j j
12 8,404 2
f 0 l
128,434 3
1 24, 1 5 f
124, 079
1 5 9, 41 8
15 9 , 3^1
IX
VIII
_ +8
80, 642
128,464 4
124, oof
159, 3,41
VII
0 4 8
80, 690
_ 5 0 1
128,494 6
12 3, 93 f
159, 24<f
VI
„ LTs
80,738
128,5 2 4 i’
12^858
1 5 p, 1 8
V
80, 7 §6
1 28, 5 55 0
123, 784
159, 1 3 0
IIII
80, 834
128,5^ 2
123,710
1 5 9 , O f £
IU
8 0, 8 S 2
128,615 4
123 ,6\j
1 5 9, 016
II
8 0, 9^3 0
1*8,645° 7
123, 5^3
15 8,959
I
s©, 97$
128,676 0
158, 902
* 1
congrua
Bali
R e s 1 d v A
dati
Io aci-
?AJ M>si
suum
E CANONE S I-
Beifts
Perpendiculum
IOO, OOO
Hypotemtf
secfnv^c
S E HI E
Faecundiffirnoque
F. CANONE FiECVNDO
Bajis
Hypotenufet
IOO, OOO
Perpendiculum
TEATIS
FiEaindiiTimoquc
E CANONE MCVNDO
Hypotenufet Perpendiculum
IOO, OOO
Bajis
SCRVP.
LL
P ART.
TRIAMGVLI pLANI RECTANGVLI
congrua
Perpendiculo
PEB.IPHEB.IA
:ommo- *
O.ircu-
grum.
nufa; con-
Hypothe-
Ius redtus
part.Angu
circuli xe.
Quadrans
CANON <zM athe m aticfs.
Qjjadrans
eirculi xc-
part.Angu
Ius reftus
Hypothe-
nufa; con-
gruus.
Cirtu-
RIANGVLI PlANI RECTANGVLI
comrno-
PERIPHBRIA
Perpendiculo
congrua
c»
Hypotemf
IOO, QOO
Perpendiculum Bafs
Bafs
IOO, ooo
Perpendiculum Hypotenuft
Perpendiculum
IOO, ooo
Bafs Hypotenufx
PA RT.
XXXIX
E CANONES I-
nuum
E CANONE F£CVNDO
Fjecundifiimocjuc
S CRJ E *
E CANON E FxECVNDo
Fxcundifliraoquc
S C RVP.
PF^TM^A
s ner n d a
TERTIA
lo ad-
dari
a.B SID VA
Bafi
congrua.
«Quadrans
circuli xc.
pare. Angu
Ius rectus ,
Hypothe-
rmia con
jjruus.
XXX
XXXI
XXXII
XXXIII
XXXIXII
XXXVII
XXXVIII
XXXV
XXXVI
XXXIX
XL
XLI
XLII
XLIII
XLIIII
XLV
XLVI
XLV1I
XLVIII
XLIX
L
LI
LII
LIII
LIIII
LV
LVI
LVII
LVIIl
LIX
LX
! i
congrua
Bafi
USSiSYA
dati
load-
$EV, AD TRIANGVLA.
Triangvli Plani Rectangvli
commo-
PER.IPHSR.IA
Perpendiculo
congrua
Hypotenuft
IOO, ooo
Perpendiculum Bajis
Bafis
IOO, ooo
Perpendteulum Hypotenuft
, Perpendiculum
IOO, OOO
Bafis Hypotenuft
PART.
E CANONE SI-
E CANONE FACVNDO
E CANONE FAECVNDO
XXXIX.
nuum
Vaecundiflimoquc
lacmidiilimocjue
sttjt
Scrtp.
PXJMist
5 EC V N D
TEUJl^i
lo ad»
dati
J.IS 1 DV 4
Bafi
congrua
6 5, 6 08
77, 162 5
82, 434
129, 596 7
I 2 I, 3IO
i 15 7. 213
% %
6 3, 6 30
63,63 \
1 * f
77, 144 0
1 8 6
77, 12 5 4
82, 4§ 3
4. 8
82, 531
J I I
129,627 8
i 1 1
129^63% 9
7 o
12 I, 238
7 *
Iil, i< 7<7
15 7 , 15$
S f
137, 103
d $, 6j 5
63, 6 9 §
I S f
77, IO <7 Jp
1 S y
77, oSS 4
82, 580
A* 9
82, #29
7 ' 7 '
129, <790 1
? I X
I 2 9, 72 I z
7 *•
I 2 I, 094
7 »
I 2 I, 0 2 5
1 5 7 , 047
, * f
136, 992
% %
63, 720
% X*
6 3, 742
1 S y
77, 0&9 9
I 3 6
77 > 05 i 5
82, 67%
0 4 - 9
8 2, 727
129,732 4
129,7^3 7 *
7 1
120, 951
120, 879
I f dy 9 3 £
156, 881
63,763
% X
6 3,787
77.032 §
1 8 <S
77 , 014 2.
0 +2
82, 776
82, 825
j i a
1 29, 8 14 9
129, 84^ 1
120, 808
7 1
120, 7 3 <7
156, 82^7
156, 771
1 $
63, Sio
63, 832
- * 8
7 d >99 f 7
1 t «
76,977 1
82, 874
0 4-9
82,923
129, 877 5
t * *
129, 908 8
7 i"
120, < 7 63
7 i
120, 593
f f
1 5 6, 716
1 56, 661
X X
6 3, 854
d 5 , S77
It c
Id, 93% 5
1 * V
7 < 7 , 940 0
82, 97I
f O
83,022
* 1 j
129,940 1
t 1 4
129,971 *
7 ~I
12 0, 5 2 2
120, 45 i
^ * *
1 5 6, < 7 o <5
, i f
1 5 6, 5 5 1
63, 8 99
^ 1 1
6 3, 922
1 8 C
7 dT, 9 2 I 4
x S «
7 < 7 , 9 0 2 8
0 49
83. 07I
0 49
83,120
t * +
I 3 0, 00 2 5)
1 * f
1 30, 0 34 4
120, 379
7 *
120, 308
„ f f
156, 49<7
, r 4
156, 442
X X
i l
3 >
1 8 *
76, 884 2
X 8 <S
76, S 63 6
n 4-9
83, x<?9
83, 2 1 i
t « t
130, Od$ 9
i » f
130, 097 4
120, 237
7 1
120, i 66
1 5 < 7 , 3 8 7
5 f
I5<7, 332
d3, 989
X X
<?4, 0 1 1
is 7
79, 846 t>
x 8 er
76, 828 3
83, 26%
0 49
83, 317
130,128 8
* 1 f
1 3 0, i< 7 o 3
7 x
12 0, O95
7 *
120, 024
f s
i $6, 277
f 4
156, 22 3
d 4 033
X i
<74, 05 <?
X 8 <5
77 , 809 7
X 8 C
76,791 1
83, 3 66
0 49
83, 415
1 1 U
130, 19 1 8
j * «
150, 22 3 4
119, 953
7 »
119, 882
156, 1 6 §
156, 1 14
<74, 078
X 1
6*4, foo
1 8 s'
76 , 77 2 5
x 8 7
76,73 3 8
83,463
83, £14
J I 6
130, 25 5 0
I 30, 2§<7 7
Ii 9, 8 ii
7 X
II 9, 740
5 y
1 5 6, 0 5 9
^ f +
156, 005
£ 4, 123
64, 145
18«
76,7 33 *
x # 7
76, 7 l6 \
8 3 , 36 4
n 49
83, <713
■ j 1 7
130, 3 l8 4
t 1 7
13 0, 3 50 t
7 . x
119, 669
1 1 9 > 599
155, 95 1
155, 897
X x
64, 167
. 4 *
04, 190
I s"
76. 697 9
x 8 7
76, 67 9 2
83, < 7 <72
83,712
130, 3^1 8
t * 7
130, 4^ 5 7
7 A
1 19, 528
119,457
155, 843
14
15 5 , 7^9
64, 212
X X
*2r ^
X X
64, 2 5<?
, i }
64? 2 79
187
76, 660 5
x 8 7
76, 641 8
83, 76I
83, 8l I
} 1 8
130,445 3
J * *
130,477 I
I19, 387
• 7 X
XI9, 3 i <7
155 , 734
i 5 5, < 78 o
I g 7
76, 623 1
s S <? I
7 6, 604 5 |
83,8^0
1 0
8 3, 910
Ji 8
130. 50 g 9
i 1 5
130, 540 8
7 0
II9, 24<7
XI 9 , 175
155.626;
r 4
155 . 57 *
XXX
XXIX
XXVIII
XXVI
XXV
XXXIII
XXIII I
I
XXII
XXI
XX
XIX
XVIII
XVII
XVI
XV
XIXII
XIII
XIII
XI
X
IX
VIII
VII
VI
V
IIII
III
II
JP 1J M
nuum
CANONE SI-
Bajis Perpendiculum
IOO, ooo
Hypotenuft
sEcrUD^e
FarcuncUfs im&que
E CANONE riCVNDO
Bajis Hypotenuft
IOO, ooo
Perpendiculum
TESJI^f
Tx dun Ii flim 6 eju c
♦
S C R VP,
L.
E CANONE FACVNDO
Perpendiculum Hypotenuft
IOO, ooo
Bajis
TR iangvli Plani Rectangvli
PART.
congrua
Perpendiculo
PEIUPBEIUA
commo-
~ Circu»
grlms ,
n u fx cotl-
Hypote-
lus redtus.
part.Angt}
circuli xo
Qu_adrans
J
CANON zMArHEMATICVS,
Triangyli Plani Rectangvli
Cimi- .
lo ad-
Quadrans
circuli xc.
■arc.Angu'
lus re&us ,
Hypo te-
nuis con-
gruus.
commo-
PERIPHZRIA
Perpendiculo
congrua
Hypotenujx
100,000
Perpendiculum Bajis
Bajis
ioo, 000
Perpendiculum Hjpotenujt
Perpendiculum
100,000
Bajis Hypotenujx
dati
HX IIDYA
Bafi
congrua
PAK.T.
E CA>
IONE Si-
um
E CANONE MCVNDO
I'i£cundilsiiu6t]uc
$ E gj E
SECFND^i
E CANONE IACVNDO
Fscundifsimoquc
TB^Tt w 4
XL.
S C R V P.
❖
54,2 79
75 , 504 5
8 3, 910
130, 540 8
| 1 19, 175 , 15 5 . 572
LX
•
I
II
2 . Z
54, 50I
54, 325
2 S 7
75,585 8
18 s
75, 557 0
f »
8 3, 950
84, 009
* 1 9
130, 572 7
< * 9
130,504
7 *
I 19, 105
7 »
I I 9 . 0 3 5
15 5 . 518
155,465
LIX
LVIII
III
IIII
54, 345
54, 3 58
18 7 1
76, 54 8 3
1 S 7
75, 529 6
84,059
4 * 9
84, 108
? 1 9
130, 535 5
1 1 9
1 3 0, 558 4
7 *
1 1 8, 954
11 8, 894
? +
155. 4 1 1
S 4 -
1 5 5 . 3 57
LVII
LVI
V
VI
54, 390
z i
54, 412
I S 7
75, 51° 5)
1 S 7 •
75,492 Z
84, 1 5 S
s ®
84, 208
* » ®
I 3 0, 700 4
J 3 O
130,732 4
7 «> :
1 1 8, 824
7 0 ■
11 8, 754
5 4
155, 303
S 4
I? 5 , 249
LV
LIXII
VII
VIII
54, 42 5
54,457
76,473 4
187
76,454 7
84, 2 5 8
84, 307
130,764 5
130, 796 5
1 1 8, 584
7 *
11 8, 5 14
155 . 196
155 , 143
LIII
LII
IX
X
54,479
z z
5 4, 501
188
7^43 5 5 >
J 8 7
75 , 417 1
8 4 . 3 57
84,407
1 3 0, 828 d
5 % X
1 30, 85 o 7
11 8, 544
7 0
118,474
155 . 089
15 5 , 0 35
LI
L
XI
XII
5*4
z %
<$ 4 > 5 4 ^
'18*
75 , 398 4
I 3 S
75 , 379 6
8 445 7
84 507
1 30, 892 8
i
130,925 0
7 «
1 1 8, 404
118, 334
A *
154, 982
154, 929
XLIX
XLVIII
XIII
XIIII
54, 558
54, 590
i H 8
7 5 , 360 8
( S 8
76, 342 O
„ +9
84, 5 5 6
S 0
84, 5 o 5
S i *
I 3 0, 9 5 7 i
J 1 X
130 , 989 4
„ 7 °
118, 254
7 *
118, 194
I 54 .- 87 S
I 54, 822
XLVII
XLVI
XV
XVI
1 z.
54, 512
54, 6 % 5
I S 7
76, $25 3
1 8 S
76’ 304 5
_ f 0
84 , 5 5 6
? •
84, 705
* * J
131,021 7
? » i
131 . 054 0
6 0
118, 125
7 0
1 1 8, 0 r 5
.* t
154 . 769
s i
154, 715
XLV
XLIIII
XVII
XVIII
54, 557
54, 579
j 3 9
75, 285 6
1 * s
75, 2 6 6 8
„ f 0
84,756
84, 8 0 6
A 1 *
131,085 3
, t i
I 3 I, 1 1 8 6
9
1 17, 985
7 0
117, 915
> 3
154, 55 3
S i
1 5 4, 5 1 0 .
XLIII
XLII
XIX
XX
54, 701
54, 723
13 3
76, 248 0
J s $
7 6, 229 z
84, 8 5 6
„ * 0
84, 906
t *■ s
I 3 I, I 50 9
I 3 I, 18 3 4
„ 7 0
1 17, 845
<r 9
117. 777
154 , 5 57
154 . 504
XLI
XL
XXI
XXII
54, 745
54, 758
I S 8
76, 2 10 4
■ I 8 9
7 5 , 191 5
84,956
_ f °
8 5, 006
i i ^
131.215 8
S i +
131,248 z
6 9
117, 708
7 0
117. 638
? i
154,451
154, 3 98
XXXIX
XXXVIII
XXIII
XXIIII
64» 79 Q
- 1 ^
54 , 8 l 2
'i 8 ' ' S
76,172 7
s S 9
76, 15 3 8
85,057
_ 1 0
85, 107
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13 I, 280 7
? r
131, 313 z
* 9
117. 5 69
< 5 T 9
117, 500
154 . 345
154, 292
XXXVII
XXXVI
XXV
XXVI
54 , 854
54 , 8 55
1 * *
76 , 135 0
is 9
76, 116 1
y 0
85 >i 57
_ 1 0
85,207
s i ?
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131, 378 3
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117,430
« 9
117. 361
154, 239
154,187.
XXXV
XXXIIII
XXVII
XXVIII
54 > 878
54 , 9 QI
I 8 8
76,097 3
18 9
76,078 4
85,257
85, 308
i t «
131,410 «j
i t es
131,443 5
<5 9
117. 292
117,223
154, 134
154, 0S2
XXXIII
XXXII
XXIX
XXX
54 , 92 3
54, 945
18 9
76,059 5
i»?
76, 040 5
85>358
85, 408
? *■ * I
131,475 I
J % 6
131, 508 7 !
CS «»
117, I54
<? 9
117, 085
154 , o2 9
153, 977
XXXI
XXX
1
tmum
E CANONE ST-
szcyNV^z
SEKjE
Excundiffimoque
E CANONE FjECVNDO
7 'E 1 {T
Fsecundi
E CANON
SCRVP.
XLIX»
mrooque
E F^CVNDO
P A R. T.
1
gruus.
nufsco.ti-
Hypothe-
Jus re&us
part.Angu
circuli xc.
Quadrans
congrua
Bali
S. S S I D V A
dati
Bajis Perpendiculum
100, 000
j Hypotenujx
Bajis Hypotenujx
100, 000
Perpendiculum
Hypotenufx Perpendiculum
100, 000
Bajis
congrua
Perpendiculo
PERIPHERIA
commo-
Circu-
Trungvli Pilani Rectangvli
Quadrans
circuli xc.
part.Angu
lus redtus *
Hypoce-
nufe .con-
gruus.
Circu-
conimo
PER.IPHER.IA
Perpendiculo
congrua
P AR.T.
XL.
S C R V P.
SEV, AT) TRI AN GVLA.
Triangvli Plani Rectangvli
Hypotenufa
IOO, ooo
Perpendiculum Bajis
E CANONE Si-
nuum
TRIMAS
Bajis
Perpendiculum
IOO, OOO
IOO, ooo
Perpendiculum Hypotenufa
Bafis Hypotenufa
L CANONE FJCVNDO
E CANONE MCVNDO
Faecundifsimdqui:
Fxcundifsimoque
s e\ie
SECr N
TERTI ^
lo ad-
daci
R 1 SI D Y A
Bali
congrua
XXX
XXXI
XXXII
XXXIII
XXXIIII
XXXV
XXXVI
XXXVII
XXXVIII
XXXIX
XL
XLI
X LII
XLIII
XLIIII
XLV
XLVI
XLVII
XLVIII
XLIX
L
LI
LII
LIII
LIIII
LV
LVI
LVII
LVIII
LIX
LX
congrua
Bafi
RES1D VA
•
dati
Io ad-
muifn
E CANONE 5 1-
Bafis Perpendiculum
loo, ooo
Hypotenufa
SECrUD^C
E*cundiifim6que
E CANONE MCVNDO
Bajis Hypotenufa
IOO, ooo
Perpendiculum
64 , 945 ! 7*> 040 6
85,408 ] 131,508 7 [
z z
^ 4, 967
z z
< 54 , 989
j 8 9
76,021 7
I 3 9
7 6, 0 0 2 8
85,458
„ * 1
85, 509
? X- 7
131, 54I 4
i t 7
131,574 I
z z
65,011
i 1
65, 03 3
1 3 9
75,983 9
18 9
75,965 0
„ 5 0
85, 559
. 50
85, 609
3 x 7
i 3 1, 666 8
} x 8
131,639 6
z z
6 5, 05 5
# z z
6 5, 077
2 3 9
7 5 , 946 1
19 O
75,927 1
„ v »
85, 660
„ y •
85, 710
S x 8
131,672 4
t x 9
131,705 3
x- ?
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75, 8 89 3
85, 761
V 0
85,811
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131,771 ©
X X
6 5, 144
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18 9
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85, 912
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65, 188
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I 90
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f 1
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131,869 8
3x9
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65, 276
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132,034 P
65, 320
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86, 267
86, 318
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132,068 O
3 ? x
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X X
65, 364
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75,680 5
75,661 5
86, 368
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86,419
3 3 x
132, I34 4
3 3 x
13 2, 167 6
X X
65,408
X %
<55,430
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75,642 5
2 9 1
75,623 4
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86, 470
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86, 521
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132, 234 Z
65,452
65,474
2 9 O
75, 604 4
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75 , 585 4
86,572
86, 623
3 3 3
I3 2, 267 5
5 J A
132, 3008
65,496
65, 5 18
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75, 566 3
1 9 1
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v *
86, 6 74
' v 1
86, 72 5
3 3 3
132, 3 34 I
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13 2, 367 5
65, 540
X %
65, 562
X 9 0
75,528 1
I 9 M
75, 509 I
86, 766
86, 827
3 3 +
13 2,400 p
3 3 y
132,434 4
65, 584
X z
6 5, 606
X 9 X
75,490 0
19 d
75,471 ©
86, 878
8 6, 9 2 9
132,467 $
3 3 y
132, 50I 3
ii 7» 08 5
6 9
117,016
6 9
116, 947
116,878
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Il 6 , 809
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11 6, 741
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116,466
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Il 6 , 5 29
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116, 056
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6 $
115,919
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6 8
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115, 375
fi 7
115, 308
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115,172
6 8
115, 104
fi 7
115,037
15 3 , 977
y 3
153, 924
153, 872
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153, 820
15 3,768
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153, 19 5
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152, 989
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152,835
152, 7 83
152, 732
1 x
152, 681
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152, 650
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152, 578
152 , 527
152,476
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152,425 j
XXX
XXIX
XXVIII
XXVII
XXVI
XXV
XXIIII
XXIII
XXII
XXI
XX
XIX
XVIII
XVII
XVI
XV
XIIII
XIII
XII
XI
X
IX
VIII
VII
VI
V
IIII
• III
II
I
♦
TERTI^t
Esecundiffimocjiie
E CANONE FVE C V NDO
Hypotenufa Perpendiculum
IOO, OOQ
Bajis
S C R VP.
XLIX,
PART.
Triangvli Plani Rectangvli
congrua
Perpendiculo
PilUPHEIUA
coromo-
Circu-
gruus.
nufecon-
Hypothe-
lus redtus
part.Angu
circuli xc,
Ojiadram
CANON (eMATHEMATICVS,
Quadrans
circuli xc.
part.Angu
Ius reSruj
Hypothe-
nufae con-
gruus.
congrua
Eafi
*.* s £Xs r A
dati
lo ad-
Triangvli Plani Rectangvli
VJ.rcu”
commo-
PER.IPHBIUA
Perpendiculo
congrua
Hypotenufi
IOO, ooo
Perpendiculum Bajis .
Bafis
IOO, OOO
Perpendiculum Hypotenujk
Perpendiculum
IOO, OOO
Bafis Hypotenufa
« 10
| ■ idasi
Usidy*
Bafi
congrua.
PA R.T.
E CANONES I-
E CANONE F1CVNDO
ECANONE FACVNDq
XLI.
nuum
Fsecundiflimoquc
s e kj &
Fsecundiffimoquc
iCiTP,
TlijMyC
SECVNVcA
■ TEXJl\st
♦ j
i.
6%, 5 o 6 ! 75,471 0 I
86,929
1 32, 501 3
11 5, 037 1 152,425
I
II
1 %
6 5 , 52 8
% z,
55 , 5*0
19 1
7 5 a 45 1 S
1 9 1
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8 6, 9 8 0
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87, 03 r
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132, 558 4
6 S
114, 969
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152, 374
t 1
152, 323
III
IIII
£$> 67 *
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1 9 i
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87, 082
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132,501 £
s s 7
1 32,53 5 5
5 8
114 , 834
6 7
I 14 , 757
4 1
152, 272
? 0
152, 222
V
VI
61,716
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87» 184
87, 2 35
i S 7
i 3 2, 559 i
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132,702 8
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fi 8
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152, 17 1
5 s
15 2, 120
' VII
VIII
1 1
6 $>759
61, 781
1 9 1
7 5 » 5 3 7 *
. 19 *
7 5 > 3 * 8 1
87, 287
87,338
j 5 7
132,735 5
i S 7
132, 770 2
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114,498
y 1
1 5 2, 059
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IX
X
XI
XII
* %
61, 803
% 2,
61, 821
J 9 2.
7 5 » 2 9 8 V
1 3 1
71 , 279 8
87, 385
87,441
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132, 804 O
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i 3 2 » $37 8
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114,43 0
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151, 918
6 1, 847
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75,250 7
1 9 1
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87,452
87, 543
i i *
132, 871 5
4 i 8
132, 905 4
« 7
I 14, 2 96
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I I4, 2 2 9
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15 1, 857
t 0
T 5 1, 817
XIII
XIIXI
3 » %
61, 851
% %
61,913
29 2
75 » “2 3
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75 , 203 2
s *■
87, 595
f *
87, 545
4 4 «
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4 4 9
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e 7
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y 0
1 5 1, 715
XV
XVI
% %
* 5 > 9 3 5
3 » E
61, 916
1 9 1
75 » 0
» 9
75, 154 8
87,598
y 1
87» 749
s i 9
133,007 0
)4 »
13 3,041 O
«s 7
IX4, 02 8
ff 7
113,951
y 1
15 I, 555
y 0
151, 515
XVII
XVIII
55,578
% %
66 , 000
1 9 »
75 » 145 *
1 9 a
75 » ia6 4
87, 801
87,852
4 4 - e
1 3 3 » 07 5 0
549
133,109 0
* 7
113, 894
6 6
I I 3 , 82 8
y 9
15 I, 555
y 9
151, 515
XIX
XX
1 %
66, 02 2
1 2 .
66, 044
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75 » 107 ^
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75» 088 0
87, 904
87» 955
440
133, 143 0
5 * 1
133, 177 t
6 7
113, 7 *i
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IT 3, 594
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15 1,455
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151,415
XXI
XXII
% %
66, 06 6
66, 088
i 9 a
75,058 8
X 9 S,
75,049 <J
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88, 007
8 8, 05 9
4 4 *
13 3, 211 2
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XXIII
XXIIII
2 » . I
66, I05
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66 , 13 I
« 9 s
75 » 03 0 3
19 t
75,011 1
88, iio
88, 1 5 2
4 4 *
133 . 2 79 4
444
133, 313
113,494
1 1 3, 428
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XXVI
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& %
66, 175
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XXVII
XXVIII
% %
66, 197
66, 218
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88 , 359
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XXIX
XXX
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6 6 , 240
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lx
LIX
LVIII
LVII
LVI
LV
LIIII
LIII
mi
LI
L
XLIX
XLVIII
XLVII
XLVI
XLV
XLIIIX
XLIII
XLII
XLI
XL
XXXIX
XXXVIII
XXXV II
XXXVI
XXXV
XXXIIII
XXXIII
X XXII
XXXI
XXX
nisum
E CANONE S I-
Bajis Perpendiculum
IOO, ooo
Hypotemfn
SECVN T>
i E *./ E
Fseeundiffimoque
E CANONE FACVNDO
Bajis
Hypot emtfx
IOO, ooo
Perpendiculum
TEEJt^f
Faeeundilfim&que
ECANONE FACVND O
Perpendiculum Hy potenti fu
IOO, ooo
Bajis
s c k. y p.
XLVIII.
PART.
congrua
Perpendiculo
PEB.IPHEB.IA
comrao-
' Circu-
gruus.
nufac cots-
Hypothe-
ius rectus
part.Angu
circuKxc.
Qn.adians
Triangvli Plani Rectangvli
SEV, AT) TRTANGVLA.
1IANGVU LANI R ECTANGVI.I
Circ «- — 3o ad-
Quadrant
circuli xc.
part. Angu
Jus reftus ,
Hypothe-
nufse con-
commq-
P2SUWHSRIA
Perpendiculo
congrua
Hypotenufa
100,000
Perpendiculum Bajis
Bajis
IOO, ooo
Perpendiculum Hypotenufa
Perpendiculum
IOO, ooo
Bajis Hypotenufa
dati
MSIDTJ
Bafi
congrua
{tUliSt
PART.
E CANONE SI t
E CANONE FACVNDO
Fxcundiflitn6<juc
SEJI/ E
SECVN DyC
E CANONE F^CVNDO
pjecundiflimocjue
TEZJUA
1
XLI.
S c r. v r.
j TRJMA
'
n xxx
, 66,161
74 . 89 ? *
88,473
13 3, 519 2
1 113,029
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( XXX
-
XXXI
XXXII
t X
66 , 1 84
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88, 524
88, 576
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1 3 3 , 5 5 3 *
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13 3, 588 0
112, 963
j 6 6
1x2, 897
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XXIX
XXVIII
XXXIII
XXXIIII
X I
66, $17
X X
66, 34«^
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i 4 4
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? 4 y
I33,6f6 £
112, 8 31
<r
112,765
150, 767
1 5 0, 7 1 8
XXVII
XXVI
XXXV
XXXVI
X X
66, 5 71
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66, 595
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74.799 1
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AXX
IIIIXX
XXXVII
XXXVIII
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66 , 414
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XXIII
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XXXIX
XL
1 9 4
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88, 940
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1 1 2, 369
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150, 422
XXI
XX
XLI
XLII
66, 501
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XIX
XVIII
XLIII
XLIIII
66, 54 5
66, '1 66
66.588
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66 , 6 i o
XX
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XVII
XVI
XLV
XLVI
I “9 3 F“
74 . tf o? 7
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89» 2-5 3
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89, 306
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134,038 0
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134,072 8
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49
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XV
XIIII
XLVII
XLVIII
74 » ? 67 0
194.
74 » 547 ^
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89,410
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134» 142 S
6 tf
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XIII
XII
XLIX
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66,675
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194.
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149, 981
149 , 93 3
XI
X
IX
VIII
LI
LII
66, 71 8
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66, 740
1 9 4,
74»489 4
194
74,470 0
y £
89» 567
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89, 620
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134,247 3
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LIII
LIIII
X X
66,761
66, 783
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74 » 45 o
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VII
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LV
LVI
66, 805
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134,387 4
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149, 641
V
IIII
LVII
LVII1
66, 848
66, 870
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89, 883
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89, 935
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134,457 6
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134,492 8
fi y
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in, 19 1
49
149, 592
fS
149, 54.4.
III
II
LIX
LX
6 6, 89 1
X X
66 , 913
1 9 y
74 » 3 3 3
V 9 4
74 » 3 14 5
89, 988
y 1
90, 040
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134, 528 0
£ y £
134 , 563 3
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1 11, 126
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4. 8
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4 8
L48
I
4
| P %JM,sC
mium
E CANONE SI-
4 ECfTNDA
ieajE
Fsecundifs imoque
E CANONE FACVNDO
T E XJT /
Fxcundillimo
E CANONE I
r
mip
SCRTR
XLVIII.
'1CVND0
PART.
j congrua
Bafi
R.ISIDVA
dati
lo ad»
Zfay» Perpendiculum
IOO, ooo
Hypotenufa
Bafis Hypotenufa,
100, ooo
Perpendiculum
Perpendiculum Hypotenufa,
100,000
Bafis
J
congrua r
Perpendiculo
PSR1PHES.IA
commo-
iufx con-
-Jypote-
us re&us.
>art.Angu
'irculi xc.
Quadrans
RlANGVLI LANI ReCTANGVLI
L uj
Quadrant
circuli xc.
f 'art. Angu
u sreiftui,
Hypote-
nufz con-
gruus.
Circu-
I
II
III
IIII
V
VI
VII
VIII
IX
X
XI
XII
XIII
XIIII
XV
XVI
XVII
XVIII
XIX
XX
XXI
XXII
XXIII
XXIITT
XXV
XXVI
XXVII
XXVIII
XXIX
XXX
eongtua
Bafi
B. B S l D V A
dati
lo ad-
QANON c MA TH EM AT IC VS,
riangvli Plani Rectangyli
comma-
URIPHERIA
perpendiculo
congrua
Hypotenufa
100 , 000
Perpendiculum Bafts
Bajis
100,000
Perpendiculum Hypotenufa
Perpendiculum
100 , 000
Bafts Hypotenujk
P A R T. 1
XLII.
seivP.
E CANONE Si-
nuum
1 1(1 M
E CANONE PxECVNDO
Fxcundirsiraoque
SEl^lE
SEcy n d^a
E CANONE FxECVNDO
fxcundifsimugue
lo ad-
dati
66,915
74 , 3 14 5
X X
66, 935
66, 9 5 6
‘ y y f
74, 2 95 0
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74 > 2 7 5 5
66, 978
X I
66, 999
1 s> 4
74 » 2 5 6 1
l 9 f
74, 2 3 6 <r
6 7, 021
% l
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74 , 2 I 7 I
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67, 064
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1 9 y
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67, 107 .
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6 7, 129
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74,139 1
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74, rI 9 5
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74,080 I
X X
67, 194
X i
67, 215
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» 9 y
74,041 4
X X
67, * 3 7
<57, 258
I 9 6
74.02 I 8
1 9 y
74.002 3
TT 1 -
6 7, 28 0
X X
6 7, 301
r 9 6
73,982 7
I 9
73,963 X
X X
67, 3*3
X X
67, 344
i 9 6
73,943 5
I 9
73 , 9*3 P
X X
67, 366
67, 387
1 9 y
73,904 4
196
73,884 8
X 1
67, 409
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67,430
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73,865 i
1 9 7 -
73, 845 5
67,45*
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67,473
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73 , 8*5 P
1 9 <y
73, 806 3
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67,495
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197
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67, 559
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73,747 4
< 9 7
73 , 7*7 7
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90, 093
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90, 146
90, 199
y *•
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y i
90, 304
y i
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y i
90,410
y j
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y ?
90, 569
f i
90, 611
y »
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y 4 -
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90, 887
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90, 940
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91, 04 6
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91, 313
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91, 3 66
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91,419
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91,473
t ?
91 , 5*6
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91, 580
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1 34 > 5 98 5
134,63 3 8
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134,775 *
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8
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135,238 3
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135, 274 a
i y *
135, 310 o
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13 5, 345 P
i y 9
135, 3818
$ s o
135,417 8
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135,45 3 8
. $ <> o
135,489 8
3 S I
135, 5*5
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13 5,561 P
J 6 l
135,598 O
j <$ 1
135,634 X
?rjm\a
nuum
E CANONE Sl-
Bajls Perpendiculum
100 , 000
Hypotenufa
SECVND^f
s e nj e
Faecandifsimoquc
E CANONE F1CVNDO
Bajis Hypotenujh
IOO, 000
Perpendiculum
TEMjr^f
Fsecundifsim&que
Rlll D r A
Bafi
congrua
[ 111,061 | 149,448 |
«. <, y
110 , 996 ^
<s y
1 1 0 , 9 3 i
149, 3 99
4 8
149, 3 51
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no, 867
„ 6 ' V
110 , 802
4 8
149, 3 03
4 8
149 , *5 5
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149, * 5 9
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1 1 0 , 60 7
* 4
110 , 543
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149, III
4 «
149, 06 3
s y
1 10, 478
110,414
4 = £
149 , 015
4 8
I 48 , 967
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no, 349
i +
110 , 285
4 8
I 48 , 919
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109 , 258
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109, 195
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LX
LIX
LVIII
LVII
LVI
LV
LIIII
LIII
LII
Ll
L
XLIX
XLVIII
XLVII
XLVI
XLV
XLIIII
XLIII
XLII
XLI
XL
XXXIX
XXXVIII
XXXVII
XXXVI
XXXV
XXXIIII
XXXIII
XXXII
XXXI
XXX
SCRTP.
XLVII.
E CANONE FxECVNDO
Perpendiculum Hypotenufa
I OO, OOO
fiS
PAaT,
congrua
Perpendiculo
?IRIPH£R1A
commo-
Circu-
gruus.
nufz con-
Hypote-
lus redtus
parr. Angu
circuli xc.
Quadrant
Triangvli Plani Rectangvli
SEV, AD TRIANGVLA.
RIANGVLt RANI RICTANGVLI
Quadrans
circuli xc.
part. Angu
jus reftus,
Hypothe-
rmiae con-
gruus.
<urcu-
comrao-
Hypotenufa
Bajis
Perpendiculum
Io sd-
dati
VIUIVHIKIA
IOO,
000
IOO, OOO
Perpendiculum Hypotenufa
IOO
, 000
Perpendiculo
congrua
Perpendiculum Bajis
Bafis Hypotenuja
Bafi
congrua
PART.
E CANONE SI-
E CANONE
FACVNDO
E CANONE
F^CVNDO
XLIL
nuum
* ajcundiilimo<juc
laecundimmoque
5 C R V P.
TRJM^C
SECTND
TERTI ,yf
1
, XXX
67, 5 5 9
73 . 727 7 [
91.65?
135,634 2
109, 131
I48, 019 XXX
XXXI
67, 580
73 , 708 1
91.687
i S i
135,670 4
6 4
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147 ,
4 7 I
97 2
XXIX
XXXII
X X
6 7, 602
73,68^ 4
9 1, 740
1 « x
135,706 5
_ 5 +
108, 903
147 ,
4 7
925
XXVIII
XXXIII
67 > 623
I Q 7
73. 668 7
Y 4
91.794
* «Y »
13 5,742 7
108, 940
147 ,
878
XXVII
XXXIIII
67, 645
6
73, 649 X
91, 847
1 fi i
135,779 O
108, 876
147 ,
831
XXVI
XXXV
67 t 666
x 9 T
73 , 629 4
Y 4
91. 901
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1 3 5, 815 3
108, 813
147 ,
7 $4
XXV
XXXVI
6 7, 688
I 9 7
73, 609 7
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91,955
13 5 , 85 1
108, 749
4. G
147, 738
XXIIII
XXXVII
2. I
67, 709
1 9 7
73 590 0
92, ooi
13 5, 888 O
108, < 78(7
147, <791
XXIII
XXXVIII
6 7 , 730
1 9 7
73 . 570 3
Y 4
92,062
1 fi 4
135,924 4
<5 4.
108, 622
147, 644
XXII
XXXIX
67,752
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92, 11(7
1 « 4
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s }
!°8, 559
147 ,
4 7
597
XXI
XL
67.773
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Y 4
9 2 , 170
5 « 4
135,997 2
108, 496
147 ,
4 «
551
XX
XLI
67.795
> 9 7
73 . 511
y r'
9 2 . 22 5
„ i 6
136,03 3 7
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108,43 3
147 ,
4 7
504
XIX
XLII
<77, 8 x <ST
r 9 7
73 . 491 5
f +
9 2 . 2 77
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6 4.
108, 369
147,458
XVIII
XLIII
6 7 > 857
1 9 s
73 . 471 7
Y 4'
9 2 , 3 31
1 s Y
1 3 < 7 , 1 0 6 7
„ « X
108, 30^
4. <r
147,412
XVII
XLIIII
67, 859
X 9 7
7 5 . 45 2 0
9 2 , 3^5
5 tf 6
136,143 3
_ 6 *
108, 243
147 ,
3 < 7 <7
XVI
XLV
67, 880
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9 2 , 439
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136,179 <>
<S 4*
I08, 179
147 ,
4 ?
319
XV
XLVI
67, 901
r 9 s
73 . 4 i* *
Y 4
9 2 , 49 3
1 fi 7
13 < 7 , 21(7 7
fi »
108, li <7
147 ,
4 7
272
XIIII
XLVII
67 , 9 * ?
1 9 *
73 . 3 9 2 7
Y 4
9 2 , 547
$ (S <s
136,253 z
108, 05 3
247 ,
2 2<?
XIII
XLVIII
67. 944
X 9 7
73. 373 0
Y +
92,^01
136,289 y
107, 990
147 ,
ito
XII
XLIX
67.965
X 9 8
73 . 3 5 3 4
Y 4
9 2 ,655
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136, 326 <?
107, 927
147 ,
4 7
133
XI
L
67. 987
X 9 7
73 . 3 3 3 5
Y 4
92 . 709
Y fi 3
136, 363 4
6 3
107, 864
147, o$7
X
LI
6 8, 008
19 8
73 . 313 7
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92 . 763
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6 J
107, 801
147 ,
4 *
041
IX
LII
a 1
68, 029
I 9 s
73 . 293 P
_ Y"+
92 . 817
J S 8
136,43 7 O
107, 73§
4- G
146,995
VIII
LIII
X X
68, 051
19 8
73 . 274 1
_ Y Y
92 , 872
x <V »
136,473 P
6 l
107, 676
4 «
146, 949
VII
LIIII
X I
68, 072
198
73 . 2 54 3
f £
92, 92£
5 « 9
I 3 < 7 , 5 1 0 8
I07, 613
4 - fi
146 , 90 ?
VI
LV
X R
68, 095
19 3
73 . 2 34 7
92, 980
j « 9
136, 547 7
107, 550
I46, 857
V
LVI
68, 115
198
73 . 2 *4 7
Y 4
93.034
136, 5^4
107,487
4*6
146, 8 ii
IIII
LVII
8, 136
19 8
73. 194 p
93 ,088
, 17 o-
136,621 6
107,425
146, 7^5
III
LVIII
68, 157
I 9 9
73.175 O
Y Y
9 3 . 143
I 3 6, 6 5 § 6
107, 3 <72
146,
4 fi
719
II
LIX
68, 179
1 9 8
73.155 2
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93 , 1 97
, , X 7 x
136,695 7
I07, 299
4 fi
146, 673
I
LX
i 1 1
68, 200
i 9 8
7 3 ' 1 3 5 4
Y Y
93 , 252
- i 7 t
136,732 8
107, 237
146, 628
♦
SECrtfD^t
SEK_1E
TERTEst
S C R V F.
XLVII
nuum
Faecundifs imoque
E CANONE EJCVNDO
■Fa^rundiflimonne
I CANONE 51 -
E CANONE
EAE C V N D O
PART.
congrua
Bafi
Bafis
Perpendiculum
Bafis Hypotenufa
Perpendiculum
Hypotenufa
congrua
Perpendiculo
IOO,
000
IOO, OOO
100,000
psjupheria
dati
Hypotenufa
Perpendiculum
Bafis
cofiimo-
gruus .
nufa: con-
Hypote-
lus reftus.
part. Angu
circuli xc.
Quadrans
riangvli Plani Rectangvli
iuj
'r
Quadrant
circuli xc.
fart. Angu
lu s reftus,
Hypote-
nufse con-
gruus.
Circu-
'commo-
fflRIfHlRIA
Pe rpendiculo
congrua
P ART. _
XLIII.
SCRVP.
Canon athe m ati cvs.
RlANGYLI P LANI RECTANGYLI
Hypotenufa
IOO, ooo
Perpendiculum Bafs
E CANONE Si-
nuum
P [ M.^C
Bafs
Perpendiculum
100,000
IOO, ooo
Perpendiculum Hypotenufa
Bafs Hypotenufa
E CANONE FrECVNDO
E CANONE FjECVNDO
Fsecundifsim o' que
Fseeundifsimoque
s £J\/£
sEcruv^c
TEATI
Io ad™
dati
XISIBTi
Bafi
congrua
congrua
Bafi
B.ESID v A
dati
lo ad-
♦ 1
68,100
7 3 » 135 4
1 9 3» 252
156,752 8 |
107, 257
146, 628
I
II
X l
6 8, 221
X I
68 , 242
199
7 3 » 1 1 5 5
19 8
7 3 » °9 5 7
? 4
93 » 30 *
f 4
93» * 6 o
i 7 S
13*» 769 9
i 7 *
156, 807 0
« i
107, 174
<5 i
107, 1 1 2
4-6
146, 582
4 ?
I46, 537
III
IIII
V
VI
68 , 264
68 , 285
l 9 9
73,075 8
»: 9 8
73 >o 16 0
s <s
9 3 » 4 * 5
f 4
9 3 » 4*9
!7 l
156, 844 2
i 7 l
156, 881 4
s 5
10 7, 049
« i
106, 987
4 fi
I46, 49 I
4 fi
146,445
68 , 50 6
68 , 527
1 9 9
75,056 x
i «? 9
75,016 1
93 » 524
S 4 -
93 » 578
J 7 1
1 5 6, 9 1 8 d
j 7 j
* 3 *, 95 5 P
fi i
I06, 92 5
6 J
10 6, 862
4 6
146, 399
4 6
146, 354
VII
VIII
$ 8 , 549
X I
68 , 570
• 198.
72,996 4
199
72,976 5
9 3» 63 3
95,688
i 7 ?
136,993 i
» 7 *
137,030 5
6 x
106, 800
« X
106, 758
4 S
I46, 3 08
;• + ?
146, 263
IX
X
X 1
68, 591
X I
68, 412
i 9 9
72,956 d
I 9 9
72,93 6 7
* 4
93 » 74 *
s s
93»797
t 7 *
137,067 8
i 7 4
137, 105 %
6 X
106, 676
* 5
106, 6I5
4 *
146, 218
4 1
146, 173
XI
XII
68 ,454
X i
6 8,455
199
72,916 8
1 9 9
72,896 «)
f f
93 » 852
f 4
93 » 9o6
5 7 4
15 7,142 d
17 f
1 3 7, 180 1
fi i
106, 55I
6 X
106, 489
4 s
146, 127
4 f
146, 082
XIII
XIIII
68, 47 6
X X
68, 497
x 0 0
72,876 <>
I 9 9
72, 857 O
t r
93 » 96 1
i?
94, °I6
5 7 s
157,217 d
5 7 s
137» 25 5 1
6 X
106, 427
fi i
106, 565
■4 f
146, 037
4 T
145 , 992
XV
XVI
68, 518
X X
68, 559
X 0 0
72,857 I
72, 817 i
94 » 071
f 4
94» 125
5 7 6
15 7,292 7
5 7 S
137 , 3 30 1
€ X
106, 305
6 %
106, 241
a 4 5
145 , 946
4 f
145 , 901
XVII
XVIII
68, 560
68, 581
199
7 2,797 2
i 9 9
72,777 3
t s
94» *8o
t ?
94 » 2 3 5
5 7 7
13 ^ 7,3 67 9
i 7 7
137,405 d
' 6 X
106, 179
• 6 t
10 6, 1 17
4 T
145, 856
'4 *
145 » 8ll
XIX
XX
68, 603
68, 624.
X 0 0
72 , 75 7 3
1 9 9
72,737 4
f r
94, 290
94 » 345
5 7 ^
13 7,443 *
5 7 7
I 3 7 , 48 o P
*
106, 05 6
<ST X
105, 994
4 S
145, 766
4 f
145,721
XXI
XXII
68, 645
68, 666
x 0 0
72,717 4
io 0
72,697 4
94, 400
94 » 45 5
5 7 7
1 5 7, 5 1 8 . 6
i 7 s
* 37,5 5 * 4
es x
105, 952
fi i
105, 870
4 f
145,676
4 f
I 45 »* 3 *
XXIII
XXIITT
68,688
i I
68, 709
1 9 9
72,677 $
X O O
72,657 5
f t
94 » 5 io
f s
94 » 5 6 5
i 7 9
137,594 3
5 7 9
15 7,652 2
X
105, 809
fi i
105, 747
145, 586
44
145 , 542
XXV
XXVI
68, 750
6 8, 751
IO « ' : >
72,657 5
x 0 0
72,617 5
f 5
94, 620
94 » 6 7 <?
* 7 9
157,670 x
i 7 8
I 57,707 P
105» 685
l 6 1
105, 624
* 45 » 497
4 f
145,452
XXVII
XXVIII
68,771
68, 793
X 0 O
72,5 97 5
x 0 0
72,577 5
94 » 7 3 1
i*
94» 786
5 7 9
13 7,745 «
r 8 0
137,783 8
6 Z .
105, 562
6 l
IOf, 501
145,407
44
145 » 363
XXIX
XXX
68, 814
68,8 5 5
x 0 0
72,5 57 5
X 0 X
72,5 37 4
94» 841
94 » 8 96
} 8 0
157, 821 8
_ * 8 '
I 37»85 9 .9
es x
*° 5 » 459
,
105, 378
145, 318
4 4
145 » 274
TXJMy*
nuum
E CANONE S I-
Bafs Perpendiculum
IOO, ooo
Hypotenufa,
secfnd^A;
, SESJE
Fcecundifs inioque
E CANONE F1CVNDO
Bafis Hypotenufa
IOO, ooo
Perpendiculum
TEATIS
Faecundifsimoque
E C A N O N E FACVNDO
Perpendiculum Hypotenufa
IOO» ooo
Bafs
LX
LIX
LVIII
LVII
LVI
LY
LIIII
LIII
LII
LI
L
XLIX
XLVIII
XLYII
XLVI
XLV
XLIIII
XLIII
XLII
XLI
XL
XXXIX
XXXVIII
XXXVII
XXXVI
XXXV
XXXIIII
XXXIII
XXXII
XXXI
XXX
SCRVP;
XLVI
P AlT.
congrua
Perpendicula
PEBJPHERiA
eommo-
Citcu-
gruus.
nufic con-
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SEV, AD TRIANGFLA.
JV;.
Circu-
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circuli xc.
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Hypote-
nufx con-
gruus.
XXX
XXXI
XXXII
XXXIII
XXXIII
XXXV
XXXVI
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XXXIX
XL
XLI
X LII
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XLV
XLVI
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XL X
L I
LI
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LV
LVI
L VII
LVIII
LIX
IX
riangvu Plani Rectangvli
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PER.ZPHBR.IA
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68, 899
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1 I
69, 109
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Angvlvs Acv-
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CANO N 1 ON TKJ A N GVL 0 RVM,
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Semi-Latus Polygoni inferi-
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adeomn
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ad Circulum,
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metam latens circumfcri-
pti Polygoni.
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Semi-Latus Polygoni circu-
fcripti reliquo femi- Cir-
culi.
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guli Reliqui,
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phsii i a, ad qua-
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rum adjumitur angulus
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ve
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ria e quadrante Cir-
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culi.
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45
24
2 12 9
41
LXIII
XXVIII
28
xo
6
52
58
37
3 i
54
9
;
I
7
57
15
X
52
50
37
2 7 48
x 2
LXII
XXIX
29
S
19
52
2 8
38
33
15
3 i
■
I
8-
35
4
1
48
14
35
2 3 4 ?
37
LXI
XXX
3 0
0
O
5 1
57
41
34 .
38
28
I
9
1 6
55
1
43
55
23
2 O O
0
LX
XXXI
30
54
8
51
25
48
3 *
3
6'
I
I
9
59
5 3
X
39
51
24
x s 6 29
4*5
LIX
XXXII
31
47
43
50
52
58
37
29
32
I
IO
45
3
X
35
r
12
1 5 3 13
29
LVIII
XXXIII
32
40
42
fo
19
13
38
57
52
4
I
1 1
32
31
I
32
23
30
1 50 9
52
LVII
XXXIIII
33
33
6
49
44
32
•
40
28
4
I
12
22
23
I
28
57
13
x 47 17
51
L VI
XXXV
34
24
53
49
8
57
42
0
45
V;- ' f
I
13
14
47
I
25
4 i
20
1 44 3*
25
LV
xxXVl
35
16
2
48
32
28
43
35
33
4 e —
I
14
9
5 i
I
22
34
59
1 42 4
42
LIIII
XXXVII
35
6
32
47
55
5
45
12
48
I
iS
7
4 i
I
29
37
22
1 39 41
55
LII I
XXXVIII
3 *
5 <*
23
47
i <5
5 0
4<7
52
38
f
$
I
15
8
28
I
1 5 .
47
48
1 37 27
23
LII
XXXIX
37
45
33
4<5
37
44
48
35
14
I
17
12
20
I
14
5
38
135 20
28
LI
XL
38
3 i
2
45
57
45
50
20
45
i
I
18
19
28
.
I
II
30
19
1 33 20
37
L
XLI
39
21
49
45
1 6
57
52
9
25
r-
I
19
30
3
I
9
1
20
1 31 27
19
XLIX
XLII
40
8
52
44
3 5
19
54
x
27
t
I
20
44
17
I
5
38
13
I 29 40
7
XL VII
XLII1
40
55
22
43
5 2
52
55
* 57
3
‘ J
I
22
'z
23
I
4
20
3 i
I 27 58
37
XLVII
XLII II
41
40
45
43
9
37
57
s ^
29
j L/
I
23
24
35
I
2
7
55
I 2(5 22
25
XL VI
X L V
42
25
35
. 42
25
35
X 0 0 0
1 0
0
0
X»
O
0 ! o
I
24
51
xo
IO 00
I
0
0
0
I 24 < I
IO
X L V
Resxd va.
S 1 N V s Refdua.
sinus
Fcripheria.
Totus.
F AE eundus
q
ly
■’
m
f, ...
Hypotenufa
T otvs.
Facundus Periphena.
Bypotemfk periphe -
PERIPHE RIA.
Pejidue.
I *
Refdua.
ria.
Semis Refiduse' e Se-
Sim i-Latus polygoni
Semi-Latus Polynni in-
Semi-mameter.
S E M
1 -Latus Polygoni
Semi E
Jj meter.
Educi uni Latus e
Se u l-mameter.
Semi-Latus
Folyponi cir-
Edutlum Latus
\
e
Semis Periphena; in-
mi-CircuIo.
mjcnpti reliquo jemi-Cn
- feripti.
circumjcnpti rehq
*o Je-
centro ,
cumfcripn.
centro.
tra,vel circa qua,&c.
culi.
miCirculi.
Acutus Bafeos*
Basis.
Perpendiculum.
Hypotemfa.
Basis.
Perpe.11
wcultm.
'
Hypotemfa.
Basis.
Perpendiculum.
Hy potent! fit.
Acutus Perpen-
diculi.
.
1
M A TH E M AT IC I C'k N ON IS E P ITO M E.
SE RJ ES PRJM^C.
1 1
SERIES SECHND^f. |
| SEJI/ ES TERTI
I
TRIANGVLI
P L AlN I
R E C T A N
G V L 1
Angulus ACVTVsa Perpendiculo
fubtenfas.
P e r pendiculum.
Bajis.
Hypotenufa. J
Per pendiculum.
Bais.
X
Hypotenufa,
Per pendi culum.
Bajis,
Hypotenufii.
Acutus R e l 1 qv v s fubtenfusa
Bafe.
In
adcommbdationc
ad Circulum,
Semis Peripherie, intra Vel circa quam de-
feribitur latus Polygoni, abime
Linea Rc&a-
S E m \Latus Polygoni m-
firipti.
Semi-tnfcripta.
Semi-latus Polygoni mfiri-
pti Reliquo Sctm-amtli.
Semi injcnpta Refidua .
Semi-viameter.
Si Mi-l.Atus Polygoni cir-
circumfiripti.
Semi-circumfcripta.
... | c
Ssmi*Qtrintjer,
V v f -
Eduflum Latus e cetro Ati
metam Uteris circum-
firipti.
S em 1-niAmeter.
Semi-Utus polygoni circu,-
feripti reliquo Semi- circuli
Semi-circufiriptA Refidua
Edum Latus e antro ad
metam latens emum-
Jcripti.
Semis Relidua: e SemLCirculo. •
Angulus velPES.iPHSRiAad quadran-
tem Circuli,in partibus qualium sefti-
matur
Diameter ioO, 000,000 ! Circulus cccix.
Sinvs ^/Pnguli,vcl Peri-
pherie.
sinti s Anguli Reliqui, fi»
Refidue periphene.
Totus , Angulo Reflo^ qua-
drAnti ve Circuli con-
gruus .
F AE eundus ^/Cngu\i,vel
Peripherie.
Vul
Totus Reltqif
Refid. perip
quadrati Ci
g°-
{ Angulo, vel
vt Reflo, vel
culi cogruus.
Hypotenufa Fecundi cin-
guli, vel Peripherie.
Totvs angulo ^Ccuto,Ve-
ripherieve, vt Reflo , vi
quadranti Circuli cogrum.
Fecundus anguli Reliqui ,
vel Refidue periphme.
Hypotenufa Fecundi an
guh Reliqui , vel Refidue
peripherie.
Reliquus e rcbto risi dtay i.
peripheria e quadrante Circuli,
MiUena part. Millejim*.
jX.
Partes.
Millena part. Millefma.
I*-
Milltna PART. MiUeJim*,
l X '
Milltna part. MillcfimK.
!*•
IOO, GOO, OOO
T
d^rC tuitta MU. i U eji Hi ct .
l X *
♦ ♦ ♦
Millena p
I**
x 00, c
■ KT. MiUeftm*.
100, 000
Millena PART. MiHeJima-
jX.
Millena, tart. Millcfim.i
1 X ■
" Millena part. Millefma.
l x - l x '
Millena part. MiUeJima.
2 X • I**
Partes.
M,U,h* part. MilUgma.
\ x ■
1 = 745 » 3 a 9
3,490, 659
I
II
1, 745, 241
3,489, 95 0
9 9 ’ 9 77 °
99 > 939 » 083
1 = 745 = 507
3 = 492 = 077
100, 015,233
100, o 5 o, 9 5 7
♦ ♦ 0 ♦
5 = 7-8, 995, 009
2, 853,525, 251
♦ ♦ «* ♦
5,729, 858 , 595
2, 855, 370, 758
XC
LXXXIX
LXXXV III
1 5 7 = 079 = 633
1 5 5 = 334 = 303
1,255,988
6, 981, 517
III
1 1 1 1
5, 233, 59(5
6, 975, 6-48
99, 852 , 952
99 = 75^=485
5, 240, 787
6, 992,679
ioo, 137, 243
roo, 244, 188
I, 908, 113, 581
1 = 43 °= 0 55 , 587
1, 910, 732, 274
r =45 3 » 5 5 8, 554
LXXX VII
LXXX VI
I? ?» 5 oo ? 5^7 <4
1 5 1, 843, 5 45
8, 7 2 5 , 64 6
10,471, 97 s
V
VI
8, 71 5, 5 80
10, 45 2, 845
99, 519, 470
99,452, 190
8, 748, 85 o
10, 5x0,423
• *
roo, 381, 973
roo, 550, 828
1 = 243, 005, 2 15
951,435, 447
1» 147, 371, 3 10
955,577,234
LXXXV
L XXXIIII
A > O, O9O, 3I6
j 48 = 35 2,985
12, 217, 505
13, 9*2, 5 34
VII
VIII
1 2, 1 8 « 5 , 9 34
13,917, 310
99, 254, 515
99, 0 2 5 , 807
12, 278,45 5
14, 054, 084
100, 750, 975
100, 982, 758
8 14, 434, 545
711= 5 36, 9 54
820, 550, 910
718, 529, 53 3
LXXX III
LXXX II
, 0 0 y } 0^7
144, 852, 328
I 5 . 707 » 9^3
17,453, 293
I X Ictj ftg.
X
15, 643, 445
17, 3 «>4, 818
98, 758, 8 34
98, 480, 875
15, 838,445
17, 532, 598
ror, 245, 505
ior, 542, 552
64 1= 3 7 5 = 148
56 7, 12 3 , 178
5 3 9, 245, 3 15
5 75 » 877 = 038
LXXXI
LXXX
^ 45 ’ * io?
r 4 r = 3 71 = 559
19, I98, (522
*o, 943, 951
X i
XII •
19, 080, 900
20, 791, 169
98, 152 , 718
97, 814, 750
19,438, 031
21, 25 5, 555
♦
.
101, 871, 5 70
102, 234, o 5 o
514,455,413
470, 453, 012
524, 084, 3 18
480, 973, 43 5
LX XIX
LXX VIII
-ijy, o2o, 3^0
137,881, 0 1 1
22, (589, 280
24,454, 6X0
XIII
XIIII
22,495, 105
24, 192, 190
97 = 437 = 007
97» 029, 573
23,085, 8x8
24, 9 3 2, 80 1
!
• 1
I 02, 53 O, 41 2
103, o 5 i, 354
43 3 = 247 = 5 8 4
401, 078, 09 5
444,541,145
4 1 3 = 3 5 6 , 551
LXX VII
LXX VI
-s- 3^5
1 34» 390, 352
Z6, 179, 939
27, 925, 2(58
XV DvdcCAg-
XVI
25, 881, 905
27= 5 6?, 7 54
95, 592, 583
95, 125 , 170
•
25 , 794-919
28,574, 537
1 0 3 > 527 = 61 9
104, 029, 933
•
373, 205, 081
348, 741,435
385, 370, 330
352 , 795, 519
LXX V
LXXIIII
x j ? O xi 3
130, 8 9 9, 5 94
29= 670, 597
31,415, 927
XVII
XVIII
29, 2 3 7, 170
30, 901,699
95 » 530,476
95, 105, 552
30, 573 = 0 57
32,491, 970
i
1 04, 5 59, 1 7 5
105, 145, 223
327= 085, 253
307, 758, 352
342, 030, 353
323, 606, 796
L XX III
LXXII
-R^y, ^ t? 5
127, 409, 035
33, 1 < 5 1 , 25<5
34, 906', 585
XIX
XX
32, 5 56-, 8 k 5
34, 202, 014
94, 551= 857
93, 959, 252
34,432,752
35, 397, 020
• . j,-
105, 752, 071
io 5 , 417, 775
290,421» 092
2 74 = 747 » 74 o
307. 155 = 3 S 3
292, 380,438
LXX I
LXX
± As y , (J O J y J Q
123, 918, 377
3 < 5 , <55 1,914
38, 397, 244
XXI
XXII
35, 83 ( 5 , 795
3 7, 4<5o, 55 o
rr * —
93 » 358= 043
92, 718, 385
ir
38, 385, 394
40, 402, 52 3
107, 114, 49 1
107, 853,475
f
25 o, 508, 895
247, 508, 5 91
279, 042, 800
2 55 , 945, 722
LX 1 X
LX VI 1 1
17 3 , O48
120, 427, 719
40, 142, 573
41, 887, 902
XXIII
XXIIII
1 39,073,112
40, <? 73 , < 5(54
92, 050,485
91= 3 . 54 » 546
42,447,480
44, 5 2 2, 85 8
* ,
, 4
108,535, 037
109, 453, 52 8
235, 585, 240
224, 503, 5 y 3
* 55 > 930 = 47 °
245, 859, 3.34
LX VII
LX VI
a i u ) t/ u 4 ^ * 0 y
Ii 5 , 937, o 5 o
43, ^33, 23 1
45 » 37 S, 561
XXV
XXVI
42, 25 l, 82(5
43,837,113
90, 530, 77 9
89, 879,405
45, 530, 7 55
48, 773=257
110, 337, 793
111, 2 5 q , 192
214,450, 594
205, 030, 3 8 3
235, 52 o, l 5 o
2 28, II7, 201
LX V
LXI 1 II
X-I5, I9I, 73I
^ 3> 44^» 2s
47, 123, 890
48, 8(59, *I 9
XXVII
XXVIII
45 » 399=050
48", 947, 15 <5
89, 100, 552
8 8, 294, 759
50, 952, 545
5 3, 170, 943
II 2, 232, 525
II 3, 257, 001
195, Z 5 r, 05 1
188, 072, 547
2 2 0, 2 58 , 927
2 13, 005,448
LXIII
LXI I
109= 955= 743
Tf>8. 2 T n A. Y ^
50, <514, 548
5 2, 3 59, 878
XXIX
XXXtoi;
48, 480, 96 2
5 0, 000, 000
87,451, 971
85 , 5 02, 540
5 5,430, 905
57=735,025
1
1x4, 335,412
1 1?, 470, 05 3
180, 404, 77 5
173, 205, 081
20 5 , 255 , 534
200 , OOO, OOO
LXI
t* LX
IO 5 , 455, 084
T ftA,. V T a e e*
54, 105, 207
5 5=850, 5 3 <5
XXXI
XXXII
5 1, 503, 807
52, 991, 927
85, 715, 730
84, 804, 810
5 o, o 85 , 058
52,485, 935
1
II 5 , 553, 328
117, 917, 841
155,427, 944
r 5 o, 03 3,449
I94, I60, 399
l88, 707, 985
LIX
LV 1 1 1
ji / *- y> /55
102, 974, 425
xoi, 229, 097
57 = 595 = 8(55
59, 54X, 195
XXXIII
XXXIIII
54, 4<53, 903
5 5,919» 290
83,857,057
82, 903= 75 7
54, 940, 75o
57,450, 852
119= 235, 335
ISO, 521 , 795
153, 985, 495
148, 2 55, 098
183, 607, 84 5
178, 829, 155
L V 1 1
LVI
99 = 4 8 3 = 7 67
97 , 7 3 8 , 4.2 8
( 5 x, 08 < 5 , 524
62, 8 3 1, 8 5 3
XXXV
XXXVIp»'"*
5 7 » 3 5 7 » <^44
58, 778, 525
81, 915, 204
80, 901, 599
70, 020, 755
72, 554, 253
122, 077,450
125, 5 o 5 , 798
142, 8 14, 795
- 237=638, 191
174, 344, 584
170, 130, 1 5 1
LV
L II II
95 » 993 » 109
O J.. IA.* 3 ? . 1 R c 1
(54, 577, 182
( 55 , 32.2, < 12
XXXVII
XXXVIII
< 5 o, 181,494
6 1, 5(55, 148
79= 853, 551
78, 801, 075
75, 355, 395
78, 1 28, 553
■ -i
125, 213, 55 5
12 5 , 901, 820
i
132, 704, 470
127, 994, 155
1 55 , 154, 002
152 , 425, 927
LII I
LII
92, 502, 450
< 58 , 0(57, 841
< 5 q, 813, 270
XXXIX
XL
< 52 , 932, 039
54, 278, 751
77 = 714 = 5 96
75, 504, 444
»
80, 978, 404
83, 909, 954
— ‘- 1 -- -- ,
128, 575, 95 1
130, 540» 730
1 2 3, 489, 715
1 19, 175, 350
158, 901, 573
155,572, 380
LI
L
89, 0 1 1, 792
71, 5 5 3 , 499
7 3 ) 303,829
X L I
XLII
6§, < 505 , 903
55 , 913, o 5 1
75,470, 958
74, 3 14,482
85 , 928, 574
9 0, 040, 40 3
•
132, 501, 300
1 34, 553, 273
1 15, oj 5 , 842
1 1 1, 06 r, 251
153,425, 310
149, 447, 545
XLIX ■
X LVI II
85= 521, 133
75, 049, 158
76, 7 94 = 48 7
78, (20, 8 k 5
XLIII
XLIIII
XL V 2" etrag'
58 , 199, 836
59,455, 838
f 70,710,578
73 = 1 3 5 = 370
7 *= 93 3 = 979
70, 7*0, 578
IOO, OOO, OOO
«r
93, 251, 509
95, 5 58 , 880
100, 000, OOO
1'
I OO, 4 )
OO, OOO
I 36, 732, 747
139, 01 5 , 350
riT. i.21 * e K
107, 235, 857
IO ?= 5 5 3= 034
145, 527, 915
3c43.955.657,
XLVII
X LVI
u i » / / 3 = 0 04
8s, 050,475
80, 285, 145
Resid
V A.
S I N Y s Refidue.
Peripherie.
Potus.
1
F AE eundus Refidue.
..•n 1
'y.
ffypotenufi Rejidne.
1
Totvs.
100, 000, 000
Fecundus Peripherie.
141,421, 35 5
Hypotenufa Peripherie.
Tetrsg. XLV
Per
78, 539, 8 x 5
ipheria.
Semis Relidua: e S emi- Circulo.
Semi-latus Polygoni infen
ptum Reliquo Semi-Circul
Semi-mfcripta Refidua.
Semi-Latus Polygoni tn-
feripti.
Semi infiripta.
Semi-vnameter.
Semi- Latus Polygoni arcu-
feripti reliquo fennCircuh.
Scmi-circufcripta Rrfidua.
•
Senti -s.
. 'ici er.
Eduflum Laius e
centro.
Seu l-xiumeter.
Semi-latus Polygoni cir-
cumfiripti.
Semi-circumfcriptA.
Eduflum Latus e
centro .
Semis Peripherie intra, vel circam
quam, 5 cc«
Acutus Baleos.
Basis.
"Perpendiculum.
Hypotenufa.
Basis.
Perpendiculum.
Hy potem fi.
Basis.
Perpendiculum.
Hypotenufa.
Acutus Perpendiculi,
'1
t
* * * n
m m
.
v*.,
J ■ •
*
-
• ' • -
KP*. '**"■•*
' : 'P' % I
- ,j. ■
-
.
• -‘f
• . *
. " - • *
.
■
/; V J
*
V’
C A N O N I O N
TRIANCVLORVM
Laterum Ratio-
nalium.
CANONION TRIANGVLORVM 'LATERVM RATIONALIVM
SE 1^1 ES
I.
SERJES
II.
S E Rl ES
IU.
*
-
4
&C.
i 9,98 8 , 4.8 0,000
99,999
49 , 941 , 3 76,589
O
99 , 94 . 1 , 4.0 0,0 0 0 1
X OOjOOO
x 0 0,0 0 0
14,98 S, 5 99,999
18,1 07
i 4 ji >8 5 j 6 ° o j o o°
3,113
995 >j 4 Z 4
49 , 9 * 1 , + 16,^8 9
49 , 94 i> 4 i 6,5 8 9
149 , 711 , 081,943
14 - 9 , 7 1 1 ,° 8 1 , 94-3
31,151
31,131
o
99 115 , 100,600
99,999
145 >63 5,0 1 9 , 4 ? 7
1 9 , 8 14 , 640,0 0 0
I OOjOOO
40 ,000
i- 4,78 0,7 9 9 9 9
17,831
1 4 3 78 0,8 oo } ooo
3,113
99 iji 3
145,6 3 5-119 457
14 ?>« 3 ?,H 9 , 4?7
49 , 1 17 . 045,891
49 , 117 , 043,391
5 0 , 97,6
3 0 , 976 !
o
98 , 5 O 4 . OOO, OOO
99,999
1 4 i >? 9 i j 71 °> 4 01
O
98,3 04,0 00,000
I 00,000
X 0 0 ,0 0 0
14,171,999,999
3 - 3 '9
1 4 j 5 76 , 000,000
613
98 3,040
141 ,^ 91 , 910,401
1 4 I if 9 i, 9 io, 4 oi
14 *, 391,91 0,399
14 - 1 , 391 , 91 °, 599
s >*44
6,144
o
97 , 484,8 O 0,000
99,999
137 , ? 8 l, 95?, 777
3 , 899 , 391,000
t 00,000
8000
i4,S7*,i99,999
17 - 3 39
1 4,3 7 IjZ OOjOOO
3.113
9741848
M 7 . 5 S 1 .I 35-777
137 , 381,1 3 3,777
9,30 3 , 186,13 1
9 , 3 03, 18 6, 13 I
3 0,464
3 0 ,46 4
o
19,3 3 3 , 1 x 0,000
99,999
46 711 , 131,117
O
9 (f, 66 f ,(S 00 j 000
I OOjOOO
10 0,00 0
i4U6*j1 99,999
17,0 8 3
24,1 6 6,4.00,000
3 . 113 .
966,6 $6
45 , 711 , 191 , 1 1 7
46 , 711 , 191,1 17
155 603 , 933,385
155 , 603 , 933^83
30,10 8
30,108
o
5 , 855 , 8 ^ 6, 000
99,999
9 , 186 , 314,393
O
93 , 846,40 0,0 0 0
I OOjOOO
10 0,000
1 1,961,^99,999
16,8 17
z 5 j 9 6 I ,6 OOjOOO
3 .IM
9 5 8 j,f <5 4
9 186 , 5 - 51 , 59 ;
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i
4
•
CANONION TRIANGVLORVM
"T" ~ .
1
•
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III.
SEPJES
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I. - "
-
■ V
• _ ’ r ' ,
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10,480,00-0,000
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899
100,000
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»67,771,960,001
81,910,600,000
1,01+
1,014
»67,771,1 59,999
167 , 771 , 159,999
»67,771,160,00 1
0
167,771,160^0 0 1
8 i 5 } io 4
1 o, 3 77,600,000
3,»»5
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35,119,686,541
. 16. 1,080,00 0
lf ,+71
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166,098,6 31,70 5
166 , 098. 631, 7 03
3 3,11 Q , 7 16 . 5 . 1.1
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4.0 ,000
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» 64 v 43 3 ,i 94 ,o »7
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15,344
15,344
3 1,8 86,698,8 0 3
3 1 «86,698,80 3.
164,43 3,494,017
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8 o 6^9 i 2
10,171,800,000
3-115
1 °j I 7 ,7 9 9,9 9 9
11,091
100,000
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^ 16,138,140,000
99,999
»61,776,543,937
80.691,100,000 -
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* 5 >*, 1 «
3 1 , 555,348 787
31,555,348,787
»61,776,743,9; 7
0 — ,
8o2j 8 i 6
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10,070,400,000
3,115
10,070,1 99,999
11,963
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99,999
3i 115,636,493
16,056,310,000
1 5,0 8 8
1 y,68 8
161,118 381,463
161,118,381,463
31,115,676,493
31,115,676,493
79 8^/10
« ~^r-
I 9,9 6 8,000,000
625
I 9 , 9 ^ 7 , 999 ,97 9
4.367
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79,871,0 00,000
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159,488,109,601
70,871.000,000 1
-
4,991
4,991
1 59,488,409 599
159,488,409,599
I f 9.4.8 8,40 9,tf 0 X
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79 4 j 6 i 4
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19,8 6 5 ) 599,999
1 1,707
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79,461,40 0,0 0 0
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3 1,571,315,069
15,891,480,000
14,831
14851
157,856,815,343
157,856,815,343
3», 57», 365, 069
O —
31,571,365,069
790^ 28
1 9,7 6 j 100 000
3 ,H 5
76 1 , 199,999
11,579
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1 5,8 1 0,560,0 00
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»56,13 3,419,697
79,0 51,800,0 00
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14,704
14,704
3 1,146,7^ 5,9 3 9
3 1,146", 71 T,9 3 9
0 — ■
78^432
I 9,660,8 00,000
3 >i 15
I 9 j 660 j 799 j 999
11,451
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40,0 0 0
15,718,640,000
99,999
» 54 , 618 , 611,657
78,6^4.5 ,x 0 0 OOO
14,576
14,576
30,913,764.531
3 0 , 913 , 764,5 31
154,618,811,657
154618,811 657
7 S i j, 3 5 6
1 9,5 5 8,4°°j°°o
3 ,H 5
19^55833993999
11,313
100,000
1 0 0,0 0 0
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6,1 10,488,169
3,119 344,000
14,448
14 448
153.011 404,1 1 3
~ 15 3 011,404.113
6^,1 2 0,496^1 59
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778J240
i 9,45 6,000,000
61 5
1 9 j 45 5 , 999,999
4,139
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77,814. 0 00,000
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151,414,174,401
77, 81 4, 000, 000
4,864
4.864
151 , 414,3 74,3 99
1 5.1,414,374 3 99
1 T 4 *>' 5 74 , > 4 , ° 1
»5 »,4» 4,374,40»
7 74 ,, 1 44
19,35 3400,000
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1 9 j 3 5 53599^999
1 1,067
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100,000
. .77,414,400,000
99,999
29,964,906,637
I 5,48 1,8 80,000
14,191
14. 1 91
149-814,73 3,183
149,814,73 3,183
»9,964,946,637
O
19,964,946,637
770^48
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3 ,H 5
1 9 j 1 5 1 ) 199,999
10,939
I 0 0j0 00
8,000
3,080,1 91,0 0 0
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148,143,280,577
77,0 04,8 0 0,000
14,064
14,064
5,919,739 113
5 , 919,7 3 9,11 3
»48,143,480,577
148,143,480,577
7 ^ 5 j 952
19,1 48,800,000
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10,8 I 1
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8,000
3 ,0 6 3 ,8 0 8,0 0 0
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„ 76,595,100,000
13,936
1 - 1,9 3 «
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5,866,664,663
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146,66 <s\ 1 6, ^,7 7
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1 9 ,046,400,000
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1 0,68 5
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76,1 8 5,60 0,0 0 0
99,9.99
19,0 n,i 88,137
1 5,1 3 7,x 10,0.0 0
1 3-,$ 0 8
1 3,808
145,106,141,183
145,1 06,141,1 8 3
19,011,118,137
19,011,118,137
7 5 * 7 j 7 ^°
1 8,944,000,000
615
1 8 j 943 , 9 99,999
4 ,ii»
1 0 0 000
75 , 77 ffI o 0 0,0 0 0
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»43,549,854,40»
75,7 76,000,000
4,736
4,736
143,5 5 o,° 54,3 99
143,550,054,399
»43,-550,054,401
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75 3^4
1 8,8 4 1,600,000
3 ,i 15
1 8384135993999
10,417
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40 ,0 0 0
75, 3 66,' Sfo 0,0 0 0
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5,68 0 ,0 86,149
1 5,073,180,0 0 0
13,551
i 3 , 55 i
141,001,356,113
141,001,356 113
5, 680, 094,149
18,400,471,145
749^5 ^3
1 8,73 9jioOjobo
3 ,H 5
1 83.7 3 93 1 9 9 ,9 9 9
10,199
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40 ,0 p 0
14,991,360,0 0 0
99,999
140,461,846,657
74 ,9 y6,8 00,0 00
13,414
x $.4x4
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18,091,609,3 3 i
140,463 046657
0 — ' —
140 .46 ; ,046,6 57
7 4 5 j 47 1
18,63 6,8 00,000
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1 836 ? 799,999
10,171
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40,0 0 0
14,90 9 440,0 0 0
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»38,931,915,697
74,547,100,000
1 3,196
1 3,196
17,786,415,1 39
17,786 415,1 39
»38, 93», »15, 697
» 3 ?, 93 », »» 5,697
74 ij? 7 <?
i8 ,5 3 4,400,000
5,115
i 8,5 3 4 , 399,999
10,043
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100,000
74,137,600,090
99,999
17,481,878,669
14,817,510,000
13,168
15,168
1 37,409 593,343
1 37 , 409 , 593,343
17,48 1,9 1 8.669
1748 1.91 8,669
7 3 7j » 3 0
1 8,43 1,000,000
61 y
18343 1 , 999,999
3,983
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7 3 ,71 8,0 00,000
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» 3 5,895.149-60 1
73.718,000 000 ,
4,6 0 8
0 8
1 35,895,449 599
1 35 , 895 = 449,599
»35.895 449,601
» 3 5 , 8 95 , 449 , 6 oi
7 3 3 j 1 3 4
i 8,3 19,600,000
3.115
i 8 , 119 ,S 99,999
19,787
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100,000
73,31 8.40 0,000
99,999
»6,877,893,893
14,66 3,68 0 ,0 0 0
11,91 1
X l>9 1 x
1 34-389,694-463
1 34. 389,694 463
16,877 938 89;
16.877.93 8.893
729j08 8
1 8,i 1 7,i 00,000
3 ,H 5
i 8ji 17 ,1 9 9 ,9 9 9
19,659
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40 ,ooo
l^.^8i 760,000
99,999
» 31,891,117 937
71,90 8,80 0,000
,i 1,784
11,784
16,578,465,587
16,578,465,587
131,891 317.937
° 1 3 1,8 9 ».3 » 7.9 3 7
724,991
1 8,i 14,800,000
3 ,H 5
1 83I 14 j 799 j 999
19531
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40 ,0 0 0
14,499,840 000
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* 3 »- 4 ° 3 ,» 5 0 ,o »7
7 2,499 100,000 ' .
1 X,<6 f 6
16,1 8 0 670,0 0 3
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16,1 8 0 .670,0 0 9
» 3 », 4 » 3 3 5 ®,° » 7
I ; 1,40 3,350,017
7 2 o,8 9 6
I 8,01 1,400,000
3 ,H 5
I 8302133993999
19,40 3
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190,00 0
71, 089, 6 00, 000
99,999
»5,984,471,141
1 4,4 17, 910,000
1 l,y 18
11,518
119,911,760,703
1 19j9» 1,760,70 3
»5,984,551,141
» 5 , 984, 55 », » 4 »
716,800
I 7,9 10,000,000
115
1 ' 7 , 919 , 999,999
77 1
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100,000
71, 680, 000, 000
99,999
X X 8 ,4 f 3 , f 6 0,0 0 I
7 1,6 8 0,0 0 0,0 0 0
896
896
118 , 453 , 759,999
, 1 18,45 3,759,999
1 18,45 3.76 0,001
“ 1 1 8.45 3,760.0 0 1
71 1,704
1 7,8 1 7,600,000
3,115
17,8 17, ! 99, 999
19,147
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lo 0,0 0 0
7 1,1 70,40 0, 0 0 0
99,999
»5,397,309,581
14,1 54,0 80,000
11,171
U,171
1 16,986 747 90 3
1 16,986,747,90 j
»5,397,349,581
15 , 397 , 349 , 581
708 ,608
17,71 5j100,000
3,115
17,71 5 , 199,999
x 9,0 x 9
X OOjOOO
40 boo
14, 171,160,000
99,999
»»5,53 »,»»4,417
70,860,800,00 0
11,1 44
11,144
15,1 06,164 883
15,1 06 164,8 8 3
115-53 »-? »4-417
1 15,5 3 1,3 24,41 7-
704,5 1 2
I 7,6 I 1,8 OCjOOC
3,115
S 18,891
I OOjOOO
40 . OOO
14,090.140.0 0 0
99,999
114,084,089,537
^ 70,451,100,000
11,0 16
11,0 16
14,816,8 59,907
14,8 16,859,907
x 2*4,084,189,537
114,084,189, 5 37
700,4 I 6
1 7,5 1 0,400,000
3,115
J 7 j 5 10,3 99,999
■ — aff*.-
1 *,763
IOOjOOO
190,005
70,041 ,6 0 0,0 0 0
99,999
»4 5» 9,088,653
14, 800, ?lo, 000
1 1,88 8
11,888
111,645,643,263
111,645.643,163
14,5 1 9.1 18.65 3
14,5 29,1 2 8.6^ 3
696^10
„ ffii
T 7 '.AOo 000 . 000 '
3,717
- 1-7 AOTiflOO.oflo -
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lo 0,0 0 0
69,6 3 2,000,000
111,115,1 8 5,60 1
6 9,6 32,000,000
4,3 5 2
x / *y y y y 7 7 7
111,115 385,599
111 115,385,599
121,215,385,601
~ 111,11 5,385,601
691,114
3/1 x i
T 7 .? 0 (^ 00.000 —
- I 7 JO(.^OO.Ofl£
18,507
IOOjOOO
»00,000
69,1 2 2,40 0,000
13,958,663,309
I 3 ,844,48 0000
1 J * J
11,63
11,651
H 9,79 3 516,543
119, 793 . 526, 543
13,958,703,309
13-958.70 3 , 3®9
N umeri pri-
mi Bafeos.
Hypotcnufa perpendiculum
100, 006
Bafis
Bypitcnufa Bajis
100, 000
PerpcHdiculum
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100,000
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■I
LATERVM RATIONALIVM.
SERIES
L
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sekjes
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0
6 8 ,811, 80 0 , 000
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■
17,103,199,999
> 8,379
1 7 ,t-° 3 ,iqo,qqo
i *>y
688,128 !
1 1 8, 3 8 0,0 36,0 97
1 1 8,3 8 0,0 36,097
13,676.007,119
13,676,007.1x9
1,1,504
11,504
68,40 3,2 0 0,0 0 0
99,999
> >6,974,744,137
X 3,68 0,640,0 0 0
I 00,000
40,000
' 7 ,'°o, 799,999
18,131
1 7, 100,800,000
?,*iy
68 4,0 5 2
> >6 97 . 4,944457
>> 6,974,944,1 37
* 5 - 594 > 988 , 831
15-594.988.83x
11,576
11,3761
0
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99,999
4,6 2-3,11 1,641
6 7,99 3,6 0 0, 0 0 0
I 00,000
100,00.0
1 6,99*, 399,999
18,113
' 6,99 *, 400,000
5,* 15
4,6 1 3,1 19,641
4,613,119,641
1 1 3,378,141:01 3
113,578,141,013
11,148
11,148
^ 79^9 3 6
67^3 84,0 0 0,0 0 0
99,999
1 14,189,716,40 1
0
67,3 84,0 0 0,0 0 c
I 00,000
ioo,ooo
'6, 8 9 5 , 999,999
1
5,599
'6,8 9 6,000,000
61 3’
114,1 8 9,916,40 I
i 14,1 89,916,40 1
1 14,189,916,399
1 141 89,916,3 99
4,1 14
4.114
V»
CO
O
1 3,434,8 8 o,o 0 0
49,999
11,36*938341
67,1 74,40 0,000
I 00,000
1 100,000
' 6,79 3 , 599,99 9
17,867
' 6,79 3,600,000
*,*Mi
10,991
11,56 1.998,341
11, 561,998, 34 *
O
1 1 1,80 9,991,70 3
.1 1 1,809,991,70 3
19,991
67 ',744
O
66,764,8 0 0,0 0 0
99,999
111,458,161,977
0
1,670,3 91,0 0 0
i 00,0 00
8,000
16,691, 199,999
> 7,7 5 9
5 ,> 15
1 1 1,43 8 ,461,977
iii;43 8,461,977
4 , 457 , 558 , 3*9
4’457 5 5 . 8 , 5*9
1 0,864
1 6,6 9 1 ji 00,000
10 864
6 6 7, 6 4 8
0
66333, 100.000
99,999
110,073,114,177
0
1,634,108,000
I 0 0,000
8,000
'6 ,5%%, 799 ,999
I 7,1 16
1 6,5 8 8j8 00^000
5 > 13
'
1 10,075,3 I4,>77
* > 0 , 075,5 >+,>77
4,405,011,367
4,403,011,567
10,736
10,736
663 ,S 5 1
0
13.18 9,1 1.0,000
99,999
*- >,7+4,070,797
63,943,60 0,0 0 0
1 00,000
10 0,0 0 0
' 6 , 486,3 99,999
> 7,48 3
I 6,48 6 ,4.00,000
5 , > 1 3
11,744,1 1 0,797
1 >, 744 , > > 0,797
108,710,33 3,98 3
108,710,333,9831
10608
1 o, 5 o 8 J
659,456
0
6 3,3 36,0 00,000
99,999
*o 7 , 575 , 982 . 401
0
63,3 36,0 00,000
100,000
10 0,000
' 6 , 38 3 , 999,999
5 ,47 >
'6, 3 8 4,000,0,00
613
1 0 7 , 5 74 * 1 8 1 4 ° 1
>07,5 74,* 81,401
>07, 374 , >81 , 399
i* 0 7,5 74 ,* 8 t, 3 99
4,096
4,096
65 5,3 6 0
1.60 3,0 36, 0 0 0
99,999
4 , > 4*, 45 9,977
0
63, 1 16,40 0,0 00
I 00,00 0
10 0,0 0 0
' 6 , 1 * 1 , 599,999
17,117
%
1 6,1 8 x jfoojooo
5,115
65 1,264
4 141 , 447,977
4 , 2 - 4 *, 447-977
X 06,0 3 6, 1 9 9,41 3
IO 6, 03 6, 199413’
io, 55 i
10,551!
0
64,7 16,800,000
99,999
104,706,403,037
0
X 1,943,360,000
I 00,000
40,0 0 0
' 6 , 179 , 199,999
17,090
1 6,1 79,1-00,000
5 ,> 15
647,168
104 706,603,037
104,706,603,037
10,941.3 1 1,0 X I
10,941,5 n,o 1 1
10,114
10,1 14
64,307,300,000
99,999
xo 3,383,199,197
0
1 1,861,440,00 •
I 00,000
40,0 0 0
'6,076,799,999
16,97»
•
5 , 1 1 5
i
I»M » 3,3 99 197
>03.383.399,197
10,677.079,839
1 0,677,079,839
100 96
1 6,076,8 00,000
643,072
O
1 7 7 9 j 5 10,000
99,999
to -414 476',419
0
6 3 ,8 97,6 00000
I 00,000
10 0,000
' 5 , 974 , 399,999
16,843
' 5 , 974 , 4 00 J°oo
^ f I
I
1 0 ,4 1 4 5 > 6 419
10,414,316,429
101,071.381,143
101.071,381,143
19 968
> 9,968
6 3 8,976
O
6 3,48 8,0 0 0,0 0 0
99,999
1 0 0,767.93 3.60 1
0
6 3,48 8,0 00000
I 00,000
'.10 0,0 0 0
' 5 , 8 7 ', 999,999
5,545
' 5 , 8 7 i,ooo,ooo
61 3 [
5 968 !
1 0 0,76 S, 1 3 3,60 1
1 0 0,768,1 3 3 ,60 1
100,768,133,399
100,768,133,399
3,968
63 4, 8 8.0
1 1,6 I 3,6 80 000
99,$99
>9,894 581,75 5
Io
6 3 0 78,40 0000
I 00,000
1 0 0,0 0 0
' 5 , 769 , 599,999
>6,587
_
5,113
19,894,411,73 5
> 9 , 8 94 4 * >,7 5 5
99 . 47 ->, * * 5,66 3
9 9 , 47 1 > * * 5 ,66 3
> 9,7 > 1
' 5,769,600,000
19 711
630,784
O
61,668,8 00,0 0 0
99,999
98,184,161,3 37
0
> 1,5 5 5 760,0 0 0
I 00,000
40.0 0 0
' 5 , 667 , 199,999
> 6,459
1 5 ,6 67,100,000
5,1 13
62 6,68 8
98.1 84., 1,557
98 ,1 84,461,3 37
196 3 6. 8 91. 467
19,636,891,467
>9,584
1 9-584
O
6 1,1 3 9,1 00,000
99,999
96,904999,6*7
0
1 1 43 1 ,840,0 0 0
X 00,000
40,0 0 0
' 5,5 64 , 799,999
>6, 3 3 >
5 ,* 15
96,903,199,617
96 903,199,617
19,381.039,913
>9,381,039,913
>9 45 «
' 5,5 6 4,800,000
> 9,456
622,592
1 1,369,910,000
99,999
19,1 16,813. 1 0 1
61,849.600,000
1 00,000
100,000
' 5 , 462 , 399,999
I3.I03
1 J ,46 2 ,400,000
6,113
>9518
i 9.1 16,863, ip 1
1 9,1 16,86 3,X 0 1
95 . 634 , 5 l 5 ' 5 0 5
95,634,313,303
>9,318
6 I 8,49 6
O
6 1,440,0 0 0,0 0 0
99,999
94,371 640,00 1
0
<S l 4.4. 0,000,000
I 00,000
10 0,000
' 5,3 59 , 999,999
645
' 5,3 60,000,000
Ilf
94,5 7 1,840 ool
94,57*, 840,001
94,371,839,999
94 > 57*)8 3 9,999
768
768
6 x 4, 4 0 0
1 1,1 0 6,e 8 0,0 00
99,999
X 8,61 3 48 8,61 1
0
61,0 3 0.40 0.0 0 0
I 00,000
100,000
' 5,15 7 , 599,999
> 5,947
1 5 7,600,000
I Ilf
1 8,61 3,318 «ii
18 613,318.611
95 , > > 7 , 745 .» 0 5
9 5 ,** 7 , 745 »*.? 5
>9-071
19.071
6 1 0, 3 04
ffo,ffib.,8oo,ooo
91,871 034 817
6 o,l 1 1,1 0 0,0 0 0
90,634,70 3,1 37
11.960,5 10,000
17, S 8-x,l 36,8 13
59 , 59 *, 000, 000
8 3.18 3,141,60 i
1 1,7 96,4.8 0,000
> 7, 5 94,6 > 7, 5 59
38,371,800,000
85 , 769 , 511,497
99,999
99,999
9 1.871.834.817
91.871.034.817
9 °,6 54 >y°y>* 87
90,634.703,1 37
I 1, 1 14,16 0,0 o o '
40,0 o o
O
18,374,406,963
1 1,041,140,0 0 o
18,116 941,0 17
99,999
99,999
17881, 1,1 6, 813
17,88l,136,8l|
88,183,041,601
88,183,141,601
99 j 999
» 7 ?? 94 > 5 ' 7 7>3 5 9
* 7,5 94 , 6 * 7,5 5 9
83,769.111,497
99*999 —
J 83 , 769 , 311,497
3 9,8 o 1,60 0,0 o o
89)4<>y 5 784.o6 3
59 , 59 >.o 00,000
88.183,141,399
38.98 1,40 0.000
86 975,087,743
71 4, 360, 000
17,1 3 3,864499
J 00,000
>8, 374,406, 963
40,000
181 16,941,0 17
100,000
I 00,000
» 9 , 46 ^) 784 , 06 3
100,000
88,183,141,399
I 00,000
I 00,000
100,000
86,973,087,743
40,0 0 o
* 7,* y 5 ; 8 64,499
3 8. 1 6 3,1 o 0,0 0 o
84 , 575 , 945,857
1,3 10,144, 0 0 0
iiM y > 4 - 7 8, 3 1 3
99,999
99,999
84 , 575 . 745,357
84 , 575 , 945,857
5,555 >47 ° , 5 > i
i, 3 55 478,3 1 5
37 544 , 0 00,000
8 1,1 1 0,406 40 1
X 1,38 6, 880, 000
16,108,940,137
36 3 14,8 o 0,0 o o
8 l,i 1 0,106,40 1
99 , 99 ^ 81,110,406,401
99,99 n 1 6,1 08,900,137
1 , 6,1 o 8 , 94.0 ,1 5
79 , 918 , 068,417
I 1,6 5 1,64.0 ,000
> 6,9 14, 789, 1 7 1
5 7,75 3,600,000
9 3,3 86,937,8 1 3 |
I 00,000
I 00,000
4.0 ,0 O o
16 914,789,171
1 o 0,0 o 0
1 5 ,'S 5 , 199,999
1 5,051,799,999
1 8,8 16
' 4-, 9 5 °, 199, 999
1 4 , 8 47 , 999,999
*y> y ^3
18.688
3,087
), 7 >t
1 5 , T 5 yjioojooo
?>* >y
1 5,05 1,800,000 -
1 8,944
5 ,>> y
8,81 6 !
6 O 6, 2 o 8
601, X It
1 4*9 50,400,000
1 4,8 48,000,000
3,1 >y
18,688
613
1 4i745i559,999
\\ '
1 4,6 45 , 1 9 9,9 99
>5 S °7
18,431
1 y, ; 7 9
18,304
8 >,»86,937,8 r 3
37,344,000,000
8 i,t fo, 406, 3 99
» 56,9 54 > 4 ° 0 >° 0 °
81,044,701,183
11,3 04,960,0 0 o
I 00,000
I 00,000
10 0,000
8 1,1 1 o ,4.06, 599
10 0,0^
8 1 04.4. 70 1,185
4.0^0 o o
' 4 , 540 , 799,999
' 4,43 8 , 399,999
1 y,py >
i8,i 7 6
1 4> 9 1 3
*4>J 5 5:1999,999
1 4 j 1 3 3,5 99,999
1 8,048
1939
5 > 7 M
5 5 8,0 i 4 *
5 9 3,9 10
1 4i74),6o°,ooo
1 4 3 ^4?ji0070oo
i , 1 > y j
5 ,> >y
1 8
3 04
5 8 9 , 8 l 4
585 , 718
14,540,800,000 -iTiil'
' 18,17«
1 4 , 4 ? 8,400,000
5,584
14,667
1 3, 048
> 7,791
* 4 >f i 9
1 4 , 3 3 6,000,000
1 4 , 1 *? 3 ,600,000
6iy
5,584
i.ny
17,7911
581,631
577,5 3 6
5 7 3,440
5 69,3 44
79,918,168,417
36,1 I 3,1 o 0,0 o o
99,999
78,711,891,777
79,91 8,168,417
78,711,691,777
99,999 7 g >7tl< g 9 ,^ 777
1 1 ,141,1 10,60 0
Os
13,313,569,337
3 3,1 96,0 00,000
76,441,1 90,4° 1
99,999
99,999
>5,5*5,519,557
>5,5*5^569,5 57
76,440,990,40 1
76,441,190,401
^>985,^5:5,68}
1 , 14 . 4 . 6 08, 0 0 0
3,148.91 5,671
3 3,70 3,6 00 000
77 , 577 , 84^,783
33,196,000,000
76^441,190,3 99
roojooo
1 oo 3 ooo
>5.983,633,683
8,000
I 00,000
Bajis Perpendiculum
100,000
Hypotcnufa
3,148 ,9 13,6 71
1 o 0,0 o o
77,577,84^,78 3
100,000
76,441,190,399
1 4j 1 5 ',' 99,999
>7,664
14 , 028 ^ 759,955
17,5 36
I 3 , 916 , 599,999
1 3,8 1 3 , 999,999
* 4 -> 8 y
Bajis
Hypetenufa
100, 000
Perpendiculum
>7,408
i,»? *
5,456
14, 1 3 1,20 0,000 — iiLHl
3 17,664
14,028 800,000
> 7,5 3 6
565 , 1 48
561,132
1 3,9 i 6,400,000 ~ ~1
4.7,408
> 3,8 14,000,000
6 2 3
Perpendiculum Hypottnuja,
I o o, o o o
Bafis
5.456
5 5 7,0 s 6
5 5 1, 96o
Numeri pri-
mi Bafeos.
6
CANONION TRIANGVLORVM
SfiBJES
III.
548 , 8^4
5 4 4. >7 6 ' 3
x 1 * £
1 4 , 72 . X ^OOjOOO —
J J 2/, 151
5 , 1 1 5
I 15 , 200,000
5 ? 5 1 7,° 24
14,017
ih7*i 3 S99 3 999 7^7
, i.J-8 99
i i 3 6i9 } t?9>9-99 17 0 - 4
SEUJES
II.
SE XJ ES
I.
10 0,000
I OOjOOO
7 f, j I t, 9 U, 5 x 3
4.0,0 O 0
1 4-. 8 j 8 608,691
54, 8 86^4.0 0,000
7 5) 3 1 1 - 9 1 2 5 6 l 3
11,895,550,000
14., 8 3 8 , 5 o 8,59 1
99,999
99,999
6 o l>f 01,781
' 601 505 381
74,192,843,457
74095,045.4.^7
4!9i°Si,io'
601,505,581
54,476,8 00,00 o
74:195.045,457
J 4 0 j 4 7 2
15,51 6,8 00,000
5;“5
1 3,5 1 6 3 7 99y9 9 9
« 5-771
I OOjOOO
4.0,0 0 0
1 o^S i 5 .4.4.0 ,000
99)999
73,081.351,897
54,067,1 0 0,0 0 0
16,896
16,896
14.616,310,579
14,616,310,579
73,081,551897,
73,081,552,897
55 ^, 57 <?
I - 3 , 4 I 4 , 4 °°y°oo
5,225
1 3 , 414,3 99,999
15-645
I OOjOOO
10 0,000
5.3 ,6 57,6 0 0,0 0 0
99,999
14-397,650,189
I 0,7 3 1,510,0 0 0
16,768
16,7 6 8
71,978 450,943
71,978,45 0,943
14,397 690,189
14 ) 395 . 690,1 39
5 ' 5 ^480
15,51 2,000,000
525
I 3 , 3 i 1 , 999,999
1,70 3
I 0 0,000
10 0,000
55,1^8,000,000
99,999
70,883,737 60 1
f 5,148,0 0 0,0 0 0
5,528
3)323
70,883,737,599
70,88 3,737,599
70,883', 75,7,60.1
70,883,737,601
5 1 3,5 8 4
1 5 ,2 09, 600,000
5,125
I 3 , 2 ° 9 , 599,999
I 5 - 3 S 7
1 OOjOOO
10 0,000
5 1,8 3 8,40 6,000
99,999
I 3 - 979 , 442,775
1 0,567,68 0,0 0 0
16,5 I 1
1 6, f 1 D
69,797 41 1,86 3
69,797,41 1-863
1 3 , 979 , 431-773
I 3 9.5 9 481,57?
J 2 4,2 8 8
1 5,107, 200,000
5 j 1 1 5
1 3 j 1 ° 7 ,i 99,999
2 5)259
I OOjOOO
4.0,0 0 0
0
1 0 ,4.8 f>y<S 0,000
99,999
68,71 9,176,737
0
f x 4 x 8 ,Soo 5 ooo
I C, 5 84
16,3 34
13. 743 . 895 . 347
1 5 > 743)89 5>347
68,719,476,73/7
68,719-476,737
5 2 0, I o> 2
1 5,004,8 00,000
5,225
1 3 , °° 4 , 799 j 999
I 5)1 5 1
I 00,000
4.0,0 0 0
1 0,40 3,840,0 0 0
99,999
67 ) 6 . 49 , 729,217
5101 9, loo.ooo
I 5 ,i ?6
I 6 1 56
13.529,985,843
1 3,519.985,845
67,649,919-217
67,649,919.1 1 7
5 1 6jO.<j 6
1 2,902,400,000
5,125
1 2 , 9 °i, 3 99,999
i 5 . 0 ° 5
I 00,000
10 0,000
f 1 } 6 o 9,6 00,000
99,999
13,3 17-714,061
0
I 0- 4 , 5 11,910,000
16,1 1 8
16,1 18
66,5 8S, 770, 303
66,588,770,303
13 , 317 , 774,061
1 3,3 1 7 , 754 -° 6 1
O
O
O
r\
r-l
w*
1 2,8 00,000,000
25
1 2 , 799 , 999 , 999
2 0 3
I 00,000
10 0,000
51,100,000,000
99,999
67,7 5 7,800,00 1
5" 1 ,i 0 0,0 00000
118
1 1 8 i
65)5 3 5 . 999,999
65.5 5 5,999,999
655 36,0 0 0,0 0 I
65,5 3 6,0 00.001
507,904
1 2,69 7,600,000
5,125
1 2, ^ 97 , 599,999
1 2,747
I 00,000
10 0,000
7 0 79,0,4.0 0,0 0 0
99,999
1 1.898,18 3,661
10-158,080,000
2 5,872
15)372
64,491,618,503
64,491,6x3,303
11, 898, 313, 6 61
Xl.89S.j13.66I
5 0 5,808
1 2, 5 9 5, 2 00,000
5,2 25
1 2,5 9 5 , 199,999
2 2,619
I 00,000
4.0 ,000
1 0,075, 1 (7 0 000
99,999
63,477-417,217
O
50^80,800,0 0 0
1 ‘ 5 , 7+4
i 5-744
1 1,691,1 15,043
12,691,1 25,045
63,475.615,117
63 - 455,615 117
499,712
i 2,49 2,8 00,000
5,125
1 2,49 2,799, 999
12,491
I 00,000
4,0,000
0
9,994 140,0 0 0
99,999
61,417810,737
O
49,97 I ,1 O O OOO
25,616
15,616
11,485,604,147
, 1 2)485,604,147
6 1 41 8,01 0,7 3 7
61,41 Sol 0,737
49 1,6 16
1 2, 5 90, 400,000
5,225
* 2,3 9 0,3 9 9,9 9 9
22,363
I 00,000
l, 0 0 ,0 0 0
4.9,5 51 , 500,000
99,999
21,281,710,973
9,9 1 1, 3 1 0, 0 0 0
I 5, 4.8 8
15,488
& 1 ,4,0 8,8 04,8 6 5
61,408^804,863!
1 1, 1 8 1 ,760 .97 3
1 1,1.8 1,76 0.97 3
491,52°
12,28 8,000,000
615
i ijZ 8 7)999)999
2, 447
I 00,000
10 0,000
0
4 - 9 , 1 51,000,000
99,999
60,397,777,60 1
49, i f 1,0 00.000
5,072
3.072
60,597,977,599
60, 397,977,599
60,397,977,601
60,3 97 ) 977-60 1
48 7,424
12,18 5,600,000
5,225
IZ ) i 8 5 , 599, 999
11,107
I 00,000
10 0,000
48,742,40 0,000
9,9,999
1 1 , 8.79 067.789
9 , 74 8,480,000
25-252
15)25 2
59 395,5 58,945
59,395.538,945
i 1 879,1 07,789
1 1. 879,1 07,789
48 5,52=8
I 2,08 5,200,000.
5-125
i 2j08 5 } 199)999
1 2)979
I 00,000
4.0 ,0 0 0
9,6 66,56 0,0 Q 0 |
99,999
5 8,40 1,188,8 97
48, 3 3 1,8 00,000
15,104
15,104
1 I,6So, 197)779
1 1,680,197,779!
58,40 i ,488,897
O
58,401,488,897
479 , 1 ? 1
1 1,9.80, 8 00,000
5,115
1 1,980, 799,999
1 r , 35 l
100,000
40,000
9,5 84,640 ,0 0 0 1
99,999
57 , 4 i 5 , 627,457
4-7)9 15,10^0,000
14 976
14,976!
1 1,48 3,165,491
11,483.165,491]
57 , 4 i 5 , 8 i 7-457
57.415,817,457
475 ,i 5 *
x 1,8 78,400,000
5,125
1 1,878,3 99)992
1 1,723
I 00,00 0
10 0,000
4-7 5 1 06,000
99,999
451,506,837
0
380,108,800
14,848
14,843
56438,554,613
5^)438,554,613.
45 2.508,457
451,508 437
471,040
1 1,776,000, 000
6 15
1 1 , 775 , 999,999
1,3 29
I 00,000
10 0,000
4.7 , '1*04,0 00,000
99,999
55,469,470.4°!
47. 1 04,0 0 0,0 0 0
2,944
1,944
5 5 469,670,399
7 7,469 670,3 99
55,469,670,401
55,469,670 4 ° 1
466,944
1 1,67 5,600,000.
5 ,ii 5
11, ^7 3,5 99,999
1 1 ,467
I OOjOOO
10 0,000
0
46,(594,40 0.000
99,999
1 0,901,794 957
.9,3 3 8,8 80,0 0 0
14,591
14.591
54)5 ° 9 , 1 74 78 3
54,509 174,783
1 0,9 0 1,8 34,957
10,901 834957
462,848
1 1,5 7 1, 2 00,000
5,225
1 1 , 571 , 199 , 999
13,539
I 00,000
510
73,400,31°
j 99,999
53,556,867,777
46,1 84,8 00,000
14.464
14,464
84 1 81,3 59
84,181.359
5 3,557,067,777
5 3 - 557 , 067.777
4 ) 8,75 4 .
1 1, 468,8 00,000
5,115
1 1 , 498 , 799,999
I I , 11 I j
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5x0
0
7 3,40 0,310
99,999
fl , 61 3 , 249,377
45.875,100,000
14,5 56
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84,181,359
84-18 1,3 7 ?
52,61 3.349,377
52,61 3,349,377
454,656
11,56 6,400,000
“'5,215
1 1,3 9 6,5 99,999
1 1,083)
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1 0 0,0 0 0
47.46 7,6 0 0.0 00
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20,3 35,563,9*7
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51,678,019,583
5 1,6.78 0 1 9,78 5
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1 0 . 3 3 5,60 3,9 17
450,56°
1 1,2 6 4,000,000
615
1 1,263, <??<>,
2,191
I 00,000
10 0,000
45,056,000,000
'99,999
50,750,878,40.1
O
45,0 55,0 0 0,0 0 0
1,8 16
1,816
50 , 751 ) 0 , 78,399
70,77 1,078,399
50,7-5 1,078,40 i
50,75 1,078,40 1
446,464
1 1,16 1,600,000
5,215
1 1,1 6 x,5 99,999
10,817
I OOjOOO
10 0,000
44,64^ 4° 0.000
99,999
1 , 993,29 3,0 3 3
1,78 5,8 56,0 0 0
1 5 952
13,952
49,831,515,813
49,8 3 1,717.823
1 99 3,3 0 1.0 3 3
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4 4 2 , 3 ^ 8 .
1 1,059,200,000
5 ,H 5
1 I4O5 9 , 199 , 9.-99
I 0,699
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0
8.8 47, 360,000
99,999
48,911,161,857
44.1 3 6, 800, 000
1 5,814
1 5.814
9.784.472.571
9,784,472,371
48,912,361,357
48,921,361,85-7
45 8,172
1 0,9 5 6, 8 00,000
5 ,ii 5
io ,9 5 9,79 9,9 99
10,571
I 00,000
4.0,0 0 0
8,76 7,440.0 0 0
99,999
48,0 10,3 86,497
O
43 817,100,000
1 5,696
I 5 6 $6
9,604,1 17,199
9,604, 1 17,199
4. 8 , 0 10^35,4.97
48,010,586.497
4 3 4,17 ^
10,8 5 4,400,000
. 5 , 125 ! - „ r ,
1 0,443
I 00,000
100,000
43,41 7,60 0,000
99,999
9,415,399,849
8,^8 5,510^0 0
15,56-8
* ~J“ X 7 , > 7 7)7 7 7
13,568
47 ) 1 17)1 99)743
47,117 199,743
9,425,439,849
9,42 5)43 9,849
450,080
1 0,75 2,000,000
615
i °,7 5 1 , 999,999
1,065
I 00,000
10 0,000
43,008,000,000
99,999
46,141 , ool, 5 oi
45,008,000,00.0
1,688
1,688
46,141,101,599
46.141,10 1,599
46, 14 1 , 1 0 I ,6 0 I
46". 141,1 0 1 .6^0 I
425,984
1 0,649,600,000
. 5,125
10,945,599,555
10,187
I OOjOOO
10 0,000
0
41,5 98,40 0,0 0 0
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9,073,078 41 3
8 5 I 9,6 80.000
1 3,512
15,511
45.565,591,063
47,365,592^063
9,073,118,413
9,073,1 1 8,42 3
411,888
1 0,5 47,100,000
' 3,225
io ,5 47 , 199,999
10,0 59
I 00,000
4.0,0 0 0
S. 43 7,760,0 oo
99,999
44,497,171,1 37
O
41,1 88,800,000
15,184
13,184
8,899,474,117
8,899.474,117
44-497-372,1 37
„ 44.49 7.371.1 37
1 0,444,800,000
3 , 115
1 o, 4 4 4 j 7 9 9,9 9 9
9,93 1
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4,0,0 0 0
8,577,840,000
99,999
43,637,3 38,817
O
41 •>77 9i‘ 1 ' 0 0.000
4 1 7,79 1
13,0 56
15,056
8,727,507,763
8,717, 7-0 7^76 3
43-637,538,817
43,6571538,817
4,09 (5
1 0,5 42,400,000
3,225
10,3 42 , 399,999
9,80 3
100,000
100,000
41,3 69,60 0,000
99,999
s, 557 , 179,011
8,175,910,000
41 5,696
11718
1 1,918
41,786,095,10 3
41,786,095,1 0 3
8,557,219,011
8,557,119,0 11
Numeri pri-
mi Bafeos.
Hypotenujk perpendiculum
100,000'
Bafis
Uypotenujd Bajis
100 , 000
Perpendiculum
Perpendiculum Bajis
100,000 .
HypotenuTa
latervm rationalivm.
S E J{:I E S
I.
SEBJES
II.
SEI ES
III.
• . *fo, 9 ^c,ooo,obo
sx. 1 , 94.5 , 040,0 o I
iO
41 , 714 ., 6 ^ 8,177
99,999
99,999
41 , 941 , 840,0 0 1
4 I , 94 ?i° 4°, 00 1
41 . 714478.177
41 . 714 . 678.177
4 ©, 960,0 O 0,0 00
41 , 945,0 39,999
1,6 30,10 8,0 o o
1 ,66 0,986,3 17
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I 00,000
100,000
4 1 > 94 J . 0 3 9,999
8,000
1,66 0 . 986,3 1 7
g,l IO, 080 . OOO :
8.1U „S74 ) 7'o 1 "i 5 ??
8,0*19,1 to,ooo
8 ,UI ,5 54/70 i
8 , 138 , 3 . 37,197
99,999
8,111,674,701
8 , t 3 8 , 797 ,* 97
8,138,837,197
40 7 7 0.40 0,000
O
1
41 , 1 08 , 373,703
40 , 347 , 6 o o,o o o
40 , 694,1 87,98 3
40 , 140, 8 00,000
40 , 181 , 097,617
6?, 8 97,999
3 9 , 8 71,10 1,40 I
166,9 9 3,66 3
39 , 464 , 106,3 37
18,719,70?
1 ,;Si ,3 76 197
99,999
99,999
40,1 8 1 , 897,61 7
40 , 181 , 097,617
3 9 , s 7 l, 9 °l, 4 ° 1
3 9 , 871,1 o 1,40 1
99,999
99,999
39 , 464,0 06,3 37
39 , 464 , 106,3 37
1 , 761 , 348,197
8 , 018 . 160,000
8 , 076 , 419 , 1 1 ?
#
6 3 , 897.60 I
39 , 871 ,,! 01,399
100,000
100,000 — - — -
■* 41,108,373,703
1 0 0,0 o 0
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3 40,694,187,9 8 3
I 00,000
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J - 39 , 871 , 101-399
10,1 $ 9 , 999,999
10 , 188 , 799,999
511
9,61 1
11,736
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1 o, i 8 8,8 00,000
1 0 , 137 , 5 - 99,999
9,4.8 X
io,o 86 ,$ 9 9,999 Ti — -
53 ? 98,7 3 3
1 , 761,3 76, 1971
I ? 5 , ? 78 , 86 -
7 . 73 °, 94 *,* 3 ?
86 5 , 69 S, 94 J
3 8,1 7 .3,101.077
1,07 0 , 4 06,3 99
3 7,8 5 ?.59 5’ 60 1
1,17 x,o 16,70 3
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’) 7 i o . 90 l,l 3 3
7.7 ? °, 94 * > 1 ? ?
38 , 171 , 901,077
38,17 5 , 101,077
3 - 7 , 476,1 8 3,197
188 , 3 . 07 , 97 *
7 , 4 *i. I 74> 01 9
317 , 989 , 17 *
7 .? ? ?.? ? 0.819
99,999
99,999
37 . 8 ??. ? 9 ?, 601
37 , 853 , 593.601
37,45 5.98 ?,197
37 , 456,1 83.197
7 , 891 , 841,167
467 , 991,777
39 . 078 , 407,413
I OOjOOO
4.0 ,0 O O
7 , 891 , 841,167
, 100,000
160,000
J 39 , 078 , 407,413
666 , 894,3 37
?S, 674,707 .66?
171 , 739,789
7,670,610,11 1
1,078 ,406 4”!
37,8? 3.593,599
170,10 3,341
7.491,1 36,679
99,999
' 99,999
7 , 411,1 34,019 1
7 , 4 * 1,* 74 ,o 19
7,3 3 3 , 190,819
7 ,. 3 3 3,3 30,819
1.8 16,164,70 3
36,176,737,197
1,000,486,399
1 U.S87.71 3,60 1
99,999
3 g , 176, 3 33,197
1,441,719 877
I 00,00 I
I 0 9,000
100.000
38 , 674 , 707,663
40 000
7,670,610,11 1
io j °5 5 , 199,999
9 , 9 8 $, 999,999
9 , 4*9
* i ,344
1,871
1,496
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9 , $$ 1 , 199,999 7
9 . 19 *
1 1,416
9 ,H 7
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roo.ooo — -
3 37,833,393.399
40 000
7,491,136 679
37,060,870,145
1,619,947.877
$6 y 666 s 6 4, I 4 5
^6,i 7 (Sr,y 55 ,X 97
33 , 887 , 3 1 3,60 1
37,887,71 3,601
1, 1 81,6 1 0,943
37 , 300 , 789,077
471,717,667
7 , 013 . 171,33 3
99,999
99,999
i 5, 5°o, 389,057
3 3 - 300 , 789.077
7 , 013 , 111,333
7,013.131-333
10 1,611,743
1,389,311,177
1,7 1 6,40 1,66 3
34,3 71 , 398,3 37
1, 8 £o,i 37,799
1 3 , 973 , 861,401
3.061,776.38 3
? ?. 397.41 3.^*7
6 46 343 603
6,644,616,397
679,77 1,499
6,770.167,70 1
3,764,109,813
41,480,690,177
3 , 717.3 39.999
3 1,1 I 3 440.0 o 1
3,888,715,01?
3 1,746,686,977
‘ 809,715,779
6,176,766,1 1 1
99,999
99,999
1,389,3 * 3,i37
*, 389 , 31*, 137
» 4 , 33 i,* 98,3 37
34 , 331 , 398,337
99,999
3 3.973. 661.401
3 3 , 973 . 861,401
i 3,397.113,617
3 3 , 397 . 41 3,617
99,999
99,999
6,644,376,397
6,644,6*6,397
6 , 370 , 117,301
6,370,167,301
363,131,941
7.133,307.039
1,0 0 0.486,40 1
33 , 887,71 3,799
I 09,000
100,000
37,060,870,143
100,000
100,000 j
7 36 666,674 *43
9 , $ $ 0 , $ 99, 999
9 , 779 , 199,999
» 1,331
9*6 3
10,1 57,^00,000
10,086,400,000 — -
3 ,* 1 3
1 1,67 1
3, »13
1 1,60 8
10,05 5,100,000 -
9,9 8 4,000,000
3 . * 1 3
1 1,344
617
1,496
409,600
407,532
403,304
4 ° 5 , 45 ^
9,951,800,000 7"— -
9,8 8 1,600,000
3 ,n 3
11,114
9 , 72 - 7 , 999,999 -
9 , 6 7 & ,7 9 9 ,9 9 9
1,807
1,43 1
8 , 97 *
9,^1 5 , 599,999
1 1,096
8,907
x 1,0 31
8,843
9 , 574,3 99,999 7—-
11,331
40 1,408
3 9 9,5 60
19 7 ,$ 11
5 9 5 , 1^4
9,8 5 0,400,000 7
9 , 779 ,ioo,ooo
3 ,* 13
2,188
3 , * 1 3
9,71 8,000,000
1 1,1 14'
6i" f
1,431
9,676, 800,000 — 5 —
J J 3 11,0 96 ! I
5 9 5,2 I 6
5 9 1 , 1 6 8
5 8 9, 1 1 o
5 87,071
2 J 2, C
9,623,600,000 ---
^j 574 , 4 °o,ooo
031
3 ,*i 3
1 1,968
100,000
1 00,000
40,0 o o
7 , 133 , 307.039
2 0 0,000
3 7,887,3 * 3 399
436.7 11,189
7,1 o 0,117,8 1 1
1,362,638,337
3 3 ,* 13 761,665
i 00,000
I 00,000
40,0 o o
7,100,117,811
190,000
33,113,761,663
8.779
9 ,St $, 19 9,9 9 9 7 —
9 , 4-7 1,9 99,99 9
*. 74 ?
1,368
9 , 42 - 0,79 9,9 99
9 ,l 6 9 ,l 99 , 999
8,67 1
1 1,776
8,787
l, 34 °, 3 « 8,377
34 , 733.0 3 1,413
343.180,3 3 3
6,870,479,667
I 1,711
I 00,000
200,000
34,73 3 ,o 3 * >41 3
40,0 o 0
6 870,479,667
1,890,1 3 7,60 1
3 5.973,861,399
6 * 1 . 333. 177
6^.7*9,484.713
3,131,718,017
3 3,223,031,983
3,398,761,497
32,830,837,303
100,000
3 3.973.861,399
40,00 o
6, 71 9 4,84,, 71 3
9,5 * 8,599,999 -
8,313
9 , 1 ^ 7 , 199,999 7.
1 1,648
8,439
11,384
9,5 2 5 , 200,000
9 , 472, 000,000-
3-113
I 1,904
g i .3
1,368
9,420.800,000
* * * *)776
9, 5 ^3/00,000 — -
J • * II
5 8 5,024
3 8 2,976
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5 8 0,9 2 8
5 78,8 8 o
5 7 <?j 8 5 2
5 74,7 8 4
9, 5 1 8,400,000
3 ,i 19
9,267,200,000 -
1 1,648
3,113
»».384
9,1 * 5 , 999 , 999 ,
9,16 4 , 799,999
1.679
1.304
8 . 33 »
»»■436
1 o 0,0 0 o
100,000 „
5 ' 33 , 113 , 081,933
100,000
3 3 1 . 830,8 37,30 3
99,999
99,999
3 1,480,490,177
31,480,690 177
3 1,1 1 3,140,00 1
; 1,1 1 3 ,440 ,0 o 1
141,364,39 5
1,199,117,607
3 , 717 , 360,00 l
? 1,1 * 3 - 4 ? 9-999
IOOjOOO
I 00,000
8,000
1,199.117,607
10 0,000
9 , 1-1 5,5 99,999
\ \ -
9,062,499,999
8.167
ii , 391
8 ,io 3
11,318
9, 2 I 6,000,000
9, I 64,800,000
61 y
1.304
3.113
* ».436
5 7 z j 7 5 ^
v
5 70,68 8
5 6 8,640
5 6 6, 5 9 1
1 ?/oo,ooo
9,06 2,400,000
31, 1 1 3,439,999!
9,01 1 , 199,999
8,9 59 , 999,999
99,999
99,999
3 1 , 74 ^ 486,977
3 *, 74< 5 > s8g >977
6,276,5. 16,1 1 1
6,1 76,566, 2 2 I
* 33 . 340 , 31 *
-I
1,169,867,479
4 , 047 , 368,897
31,381,831,103
840,905,513
6 , 104 , 114,477
4339.389,183
5 0,661,41 o , 3 1 7
4,3 * i.» 3 3 . 3 99
30,5 0 3,846,40 1
4,661,820,863
I 9 , 94 8 . 379 .i 37
99,999
99,999
6 ,io 4 ,i 74,477
6,104,2 14,477
3 0,66 i,i 1 0,8 17
3 0,66 1 ,41 0,817
4,104,527,617
99,999
99,999
30,30 3,646,40 1
3 0,5 o 3,846,40 I
19.948.179.1 37
19.948.379.1 37
31 , 011 , 071,383
971 , 877,8 37
6,1 3 i,iS 1,16 3
8,000
1 , 169 , 867,479
100,000
100,000 —
3 1,3 81,8 3 1,1 o 3
8,1 3 9
1 1,164
31 ?
448
i 00,000
100,000
X O 0,0 O O
31 , 011 , 071.383
40 ,0 o o
4,511,153,601
30,30 3 , 846.599
931 . 564,173
5 , 989,675 817
6,1 3 1,2 3 1, 1 6 3
I 00,000
I 00,000
loo.ooo
30 , 303 . 846,399
40,000
Bajis Perpendiculum
100,000
Hypotenufa
1 , 989 . 675, 817
o o 8,0 1 I
8 ;, 908 , 799,999 7/7
$, 817 , 199,999
}6
7 ,947
1 1,071
8,806,599,999
$, 71 1,2 99,999
7.88 3
1 r ,0 o 8
7.819
10,944
$, 701 , 999,999
UJJ.
1,176
q jr 7.69*
^J ^5 2 , 7 99,9 99
3 ,* ij
* 1.391
3.1 iy
11 , 318 '
9 011,100 000 —
7 J 11 , 164 ]
8,9 60,000,000
l±l
448
8,908 800,000 — ’ ,Ily
7 7 7 11
878 5 7,6oo } ooo —
136
3 , i 1 S
1,071
5 17 4 j 5 44
5 ^ 2,496
5 60,448
5 5 8,400
5 5 /> 5 5 1
5 5 4 , 5 04
8,8 06,400,000
3 ,* iy
1 1,0 o 8
8,755 2 00 OOO — 5 f
* o, 9 44 (
8,704,000,000 —
2,1 76
Bajis Hypotenufa,
160,000
Perpendiculum
8,652 800,000 — r _Llj
* 3 3 io8is!
551,156
5 50,208
Perpendiculum Hypotenufa
100,000
Bafis
Numeri pri-
mi Bafeos,
3
CANON ION TRIANGVLORVM
544,064
5 42,0 1 6
S E ({1 E S
II I.
SEEJES
II.
4 19,963
5 i 7,9io
1 . 60 1 . 600,000 — N 1
3 19 , 752 .
8,55 0,400,000
?,i -
10,688
3 ,6o 1,5 99,9 9 9
1^,199,999
7,° »■ 7 I
10,751
7 f6;
10,688
100,000
8 , 442 , 100,000
8,448,000,000
5,225
So 61 +
<S 1 5
1,111
29*595, o°9,ol3
100,000
2 9,2+5 73®, °6?
5 5 5>S 71
5 5 ?jS2 4
? 5 1)776
5 14,718
8,546,800,000
8, 5 45,600,000
3,225
1 0,496
3,215
10-431
8 j4 99)199)9 9?
8 j44 7)999,99 9
7 7 + 9 9
1 0.6 14
Mf7
XIII
4-6,0 O 0
5,778,911,052
100,000
13,5+7, +32,599
8 , 556 , 799^99 j^|
8j545jJ9 9j999
+0,0 o 0
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iit
x 0,4;
I 00,000
200,000
5 2 7, 6 8 o
525,652
? 2 . 5 j 5 S 4
5 i t,J ? *
8.294.400.000
8.245.100.000
10,368
3,125
10,504
8 j 1 94j595,999
8 i 245 , 259 j 999
7,1+3 |
10,368 !
7,279
1 0,; o+l
x o o , O 0 c
SEI^IES I
L ' j
I
+ 81 1,390,977
99,999
2, 183, 792, 361
191,45 5, 6 S? 7
29,5 95, 0 °9>°1 3
1,183,800,361
£
1,183,800,36-1;
t
+,957,863,937
99,999
5,848 707,21 3
I
992,572.787
29,2+3,736,06}
5,8+8,747,11 3
5,848,747,113
l
I 620,447,949
99,999
28,894,360,257
I
5>l 0 l> 13 9,7+3'
5,778,921,051
28,894,560,1 57
1 S , S 94, 5 6.0 ,257;
t
5,144 5 t S,4o 1
99,999
18,547,18 1,60 1
I
5,2+4.528,399;
i8,5+7,+ 8i-599
1 8, 5+7, +8 1,60 1
18,547,48 1,60«;
l
1,076,939,981
99,999
2S,2o 1,3 00 ,097
5,3 84,699,90 3
5,6+0,500,019
1 8,2 0 1,5 0 0,097
2 8,2 0 2,5 0-0,0.97:
1
5,521,784,257
99,999
5,571,883,149
1
1, 1 04,5 56,S;5'i-
17,859,615.7+3
5,571,91 3,2 + 9
5 571.92 3,149;
I 00^000
i 7i 5iS, 818,5 + 3
50 ,000
5,436,017,699
5,658,771,457
17 518,818,54;
1,158, 5}l. }0J
8,192,000,000
615
5.436,017,699
99)999
99)999
5, 5° 3,7 1 5,709
5,5° 3,765,70 9
27,279,938,497
il
2,2« r. 754+92;
1,048
3,215
8,140,800,000 —
■ 3 " 10,176
3,H5
8.089.600.000 —
8.058.400.000
3 ,T 3 10,048
10,111
3.2 15
17,180, 1 38,497
S> 5 °3.76 5,7<>9;
5,791,661,50 3;
,19 1)999)999
$0,799)999
1.+13
1,048
7,0 5 I
, 10,176
10 0,000
100,000
J 26,843.545,599
I 00,000
+0,00 9
5,3 0 1,80 9,972
17,180,133 ,49 7
8 , 0S9, 5 99,999
8 >°5 8,199,999, 7
6,937}
I 0,1 1 1 '
6,91 3
•I 0,048
5,91+ , + 5+,+° I
16,843,545,599
l,i 1 0,8 3 0,0 1 9
5,3 o 2,809,971
99)999
99,999
26,843,345,601
26, 84}, 5+5, 601
i s, 5 08, 8 49,8 5 7
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Hjfotenufi
Bajis
Perpendiculum
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Ba{is Hypotenufa
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Numeri pri-
mi Bafcos
S
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EXPLICITVM CANONI ON TRIANGVLORVM
UTERYM B.ATIONALIVM.
*
SYNTEXIS NVMERORVM Canonij.
SEBJES ///.
Ba sit
loo, o o o
Hypoiinvsa
Aquatilis.
Quarta pars numeri
primi Bafeos duBa z> ivivjcslsdv s, C
in 1 0 0, 000. CELV M E RyST 0 R,
Proftaphxrefis.
^€dditiua,danda ex Diuifone,vel Frag.
mente numerorum,quorum
SEBJES II.
PSRFENDICVLVM
I O O, O O O
Aequabilis.
Hiiounysa
© iv
vel,
‘N.V OtERylT O R.
© I V 1 © E •& S,
Vel ,
© EK.O M
r ox*
Numerus
primus
Bafeos.
PeRPINJSICVIVAS
./liquabile.
idem Numerus , a ui m
Bypotenufa.
Proftaphaerdls,
Eadem, ^fblatiua.
Proftaphxrefis.
^fdditiua, danda ex Diuijione vel Frag-
mento numerorum, quorum
zo o, o o o
© 1 V I © E Vi. S,
•Uti,
© Ettl,0 SeC l^N-^i-
T OR.
)
f Numerus pri-
mus Perpendi-
culi ,feu, Qua-
dratum dimi-
di/ numeri pri-
mi Bafeos, mi-
\jiutu vnitate.
Basi*
9IVIT) i
SERIES I.
Hvpoti Nm
I o o, o o o
PiRPsNDienvM
Aequabile.
t o o } o o o
IDSVIVEWDVS, (T
W,
SiVAWE RySTOR,
Z O O j o o o
Proftaphxrefis.
^fblattua, Danda ex Diuijione, vel Frag-
mento numerorum, quorum
© I © / © E 22 , ,S,
Vtl,
© E 22. O AW / 22. » 4 -
roji.
'Ekvvs, r Numerus pri
i&vac erutor. \musBafeosdu-
Danda ex Diuijione, vel Fragmento nu-
merorum, quorum
jBus in
?.
I o o, o o o
© / © 7 © £ 22, tf,
vel,
ID E1E0 M 1H.U-
TOr,
Numerus pri-
mus Perpendi-
culi.
Danda ex Diuijione, vel Fragmento nume-
rorum , quorum
f Numerus pri
mus Bypotenu-
ft,feu, Quadra-
tu dimidij nu-
meri primi Ba-
feos,auBum v-
K ~-mtate
Sa sis.
viv.mvvs, (-Numerus pri-
VEvacERyiTOR. • mus B a Jies du-
Bus m
i o o, o o o
©/©/©£${, j,
vel ,
© £22.0 AW 122^-
TOR,
Numerus pri-
mus Bypote-
Qnufe.
SYNTEXIS NVMERORVM inlujlo Canone.
Cvm fint Pro fapharefes in ferie tertia fubdupla ad Facundum dimidia Refdua Peripheru, adjumantur ea abs Fragmentis,vt pete per continuam oBonarJ numeri progrejiionem,
videlicet 'i, \6, ^OytCc. donec adFroJlapharefim to. Ut deuematur.qua fere ejl fubdupla ad Facundum Periphana xxj. cum femijfe. Et locus wquem cadit Projla-
pharefs %primuseJlo , 16 fecudus ,24 tertius, & J ic de reliquis Cf erunt i,J9 l° c<t - Qui numerus accedit ad 2,70.0, numerum fcrupuloru partium xlv.cr locorum confequen-
ter,quot filent conjhtui in Canone irrationalium-, & ita Canonici numeri conflantor ,CB’ conjl ruuntor. Et Peripherta e Canembus Facundis, vti ea congruunt duplo cenjhtuarum
Projlapharefon, duplantor, Et e regione numerorum collocantor .
SEBJES III.
Basis
loo, 000'
Hipotsnvsa
Aequabilis.
Ex diuijione numeri 2,500,000,000,! conjlituta
Profiapharef. vel ,
Ex diuijione numeri 312,500,000 a numero loco-
rum.
Proftaphxrefis.
^Cdditiua,vti confituitur,C r ’ dat Numerus locorum duBus
m oBonarium,
PiRPINDICHYM.
iEquabile.
idem Numerus qui m
Bypotenufa.
Proftaphxrefis!
Eadem , ^fblatiua.
SEBJES II.
PixpeNdicylyu
100, 000
Hi POIIMYiA
SEBJES /.
Hipoiinysa
loo, 000
iEquabilis.
2 0 0, OOO
©/©/©£ 92 »©*, f Dupla Pro fa-
vi, | i l r~
•H.V ac E restor, pharcjts tertia
ProftaphxrcEs.
r JIOO, OOO
xXdditiua, danda ex Diuijione, vel Frag- J
mento numerorum, quotum f
© / v 1 © etes, | perpendiculum
© e 22, odeiiE^i I tertia fenei.
TO R,
Basi *
Aequabilis.
vividekvvs. r Quadratu du -
‘K.vatERySTOR. pia Projlapha-
QuadruplumProfapharefeos tertia feriet. \J e f eos tcrtia fe‘
Proftaphxrefis. *s
^fdditiua, danda ex Diuijione, vel Frag-
mente numerorum, quorum
Per p en dicyet
M
A£quabilc.
100, 000
© IV 1 T> EltiTO V S,
vel,
22© OC E Ryi T O R.
Proftaphxrefis.
^fblatiua, danda ex Diuijione, vel Frag-
mento numerorum , quorum
© / V 1 © f 52, S,
Vll,
©£%0 JM 17Ze%e4-
; t.or. L
Y Dupla Projla-
pharef s tertia
[feriet, duBam
J100, 000
)■
Bypotenufa ter-
tia fenei.
Aequabilis.
Basis
© IVITEIEWS,
vel,
22 V Ot S Ryi TO R^
© / © / © E 22 S,
V cl .
© E^OAYf l^yi-
TO^
Perpendiculum
\jertia feriei.
Quadruplum Profapharefeos tertia feriei.
Proftaphsrefis.
iXdditiua, danda ex Diuifone,vel Frag-
mento numerorum, quorum
© / V 1 © E OJ, s,
vel,
© E^OM l
TO R,
Quadratu du-
pla Projlapha-
refeos tertia fee-
\riei.
Bypotenufa ter-
\Jia feriei.
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F%AN C IS C I V IETJEI.
VNIVERSALIVM INSPECTIONYM
AD CANONEM MATHEMATICVM
Liber Sinmlark.
o
LVTETIiE,
^Afud Ioannsm Mettajer , in Mathmaticis Typographum Regium 3 fub figno
D. Io annis 3 e regione Collegij Laodice n/Is«
M. D. L X X IX.
S
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CAPITA JN SPECTIONVM.
TfANGVLI PLANI XECTANGVll
Diagramma Nota.
Laterum Trianguli Plani reBanguli prima gfi Pythagoraa
Analogia.
o
Norma Canonij ■ *
Triangulum Planum reBangulum Circulo adcommo datum infcriptione.
Triangulum Planum Rectagulum Circulo adcommodatum circumfcriptione.
®Ad Sjntaxim Laterum infcriptorum Kvpicorepct Geometrica pofiulata .
<zAd Sjntaxim Laterum circumscriptorum Kupiajrgpet/ Geometrica pofiulata.
Diagrammata ad Apodixim Geometricorum fofiulat orum.
Ambit iofa linea ad re Eam Analogia per plus minus .
Analogia gener ali or ftn numeris irrationalibus.
Analogia tandem Perimetri Circuli ad Diametrum .
A%Hnor~yera.
tJMdior hera. j
zStfedia fatis accurati
Sinus vnius Scrupuli.
iJMinor vero.
zSJ-faiorvero.
Adtedius fatis accurato.
Trianguli Plani reB anguli adCir culum adeommodati inferiptione, circum -
feriptioneve , Series trina Seriei oAnaloga,pro numero Laterum vel Angu-
lorum.
Canonica in Triangulo Plano r e B angulo Analogia fex Laterum gfi Angu-
lorum cum Sinu Tefiifieu Hypothetico ,6x quibus, datis prater Angulum re-
Bum latere gfi angulo, vel lateribus duobus, datur Triangulum.
<* Analogia totidem abs finu ReB i.
XI II AdSyntaxeos Normam in Analyfi, Triangula Plana reBangula tria.
A nalogia A rcbimecUa.
XIII I TRIANGVL VM Planum Obliqu angulum.
XI
XII
t ij
X V Parajcem ad feci tones Obliquangulorum.
i X htm ex Lateribus exquiruntur A nguli.
z »A\ merfParafceueJum ex Lateribus exquiruntur Ai nguli,
j Anceps Qbliquangulum.
In Qbliquanguli $ peBis in ObliquanguL frequens Marajceue.
/ In Mifcellaneis Planorum, fele Hior es aliquot A nalogi#.
Ei^lJCCOTepctj.
j . In RtSlangulo ,edudia angulo reSlo Perpendiculari.
ij, In obtufangulo obliquangulo } educi a k vertice Perpendiculari, & duabus ei Parallelis
a fingulov ddicet crure fingulagn Aqualis altitudinis fttb «quali Bafi.
iij. In Obtufangulo Obliqu&nguio , educ Ia a vertice Perpendiculari , & duabus ei Parallelis
a fmgulovidelicet crure fmgula, aqualis altitudinis fub in&quali Rafi,
iij. In Redi angulo vel Obliquangulo, intra quod deferibitur Quadratum .
v. In q ua d nfecio k Duabus diametris Circulo.
r-epyixcbrzpcLj.
/. In Linea fella.
ij. In Linea jedia, media & extrema ratione,
iij. In duabus lineis,
iiij. In tribus proportionalibus,
v. In quatuor continue proportionalibus,
vj. Se di io Quadrati .
vij. Ssdlio Cubi.
4 Quatuor continue proportionalium Diagrammata.
7 Ex dato Reclangulo, aquali ci, quod jub lateribus continetur, cum differentia, hei aggregato
eorundem , dantur Latera.
$ Ex dato Re clangulo, aquali ei quod fub lateribus continetur \cum ratione eorundem , alterius
ad alterum } dantur Latera.
7 Regula quam vocant, Falf.
i
X VI Plani obliquanguli in Obliquangula fedi Thsoria, adfequendi methodus
aliquibus datis.
XVII TRIANGVL VM SPHjERICVM RECTANGV-
LV M.
XVIII Trianguli Sph #rici reB anguli decem AA ei amorpho fes.
X IX Qanonic# decem inSph#nco Triangulo ReB angulo iam diu expetit#, necdum
ante hac exhibita Analogi# ffexies etiam pro numero Terminorum repetit#,
ffuarum duBu,fi ex terminis Sph#r ici Trianguli reBanguliffuo quilibet 3
prster Angulum reBum dentur , Atro qu#fitm terminus , vel ex vnd opera-
tione Logijl icesffiue ^Multiplicationis ffiue Tiuifeonis ,vtra commodior vi-
debitur , vidjnnotefcit .
X X ^Analogia fexdem abs Sinu Recfifm Xoto.
XXI Cum quadrato Sinus relti Analogia dua.
XXII Cum finu toto., gf eiufdem quadrato Analogia dua.
XXIII XRI A N G V L V Ai Spharicum Obliquangulum .
i Termini analoza ferte.
di
AAetathefis trium cl
3 Eduftio Qnhogonij.
z XAetathefis trium datorum terminorum.
XXII II Ad feffionss 0 bl i 'qu angulorum in Reffiangula,Farafcem.
i Ex coaceruatione duarum Per plenarum, & ratione Sinuum eorundem , dificernuntur ‘Pe-
ripherie.
z Ex differentia duarum T eripheriarumjf) ratione Sinuum e arundtm, dantur Peripherie.
5 Ana logia Angulorum, in fiePhone , quam proflat perpendere ,dum ex Angulis eruuntur La-
tera.
-f Se Aio Trianguh J. itorum Laterum 3 ad adfiquendos Angulos,
j Aliter, Parafceue dum ex Latenhus Anguli.
L Pyurfus , A i e Lateribus eruantur anguli , Analogia in Obliquangulo,cum quadrato Sinus
reAi.
7 Analogia denique figmentorum Bafieos & Crurum in anguli njcrticis bifeclione.
XXV FRIANGVLVM F L AN I-S FHAERICVM.
i In Plani fighericis KaQoAixdrepcb.
z At P 'eripheria reuocetur ad panes Diametri, (ff e contra adpofiti Numeri.
3 A tfiecenrur magut.il /iis media extrema ratione , vel feile compleantur, vel etiam conti
mute d continuatione jegrrgentur , adpofiti Numeri .
jf Geodefia Triangulorum .
Simplex.
Comparata .
S. JintTr ungula aeque alta ve' Juh aquali Baji,
Si ^/Chgulo yi ngulurn. habent aequalem,
wtd queatis Triangula.
j Geodefia Circuli.
6 Geodefia Spherarum.
7 Ad Circulos fiuperficiefique Spherarum e Diametris, harum fioliditates *e Cubis 3 & e cen-
tra, adpofiti Numeri.
t Ad SpheraS e Diametris & e contra, Archimedea menfiura.
S Quadratura Hippocratica Memfici .
10 ‘Parabole.
11 Qp^dratura Paraboles Euclidea
12 Latus Quadrati Circulo circum ficripti,infcripti,$) equalis.
t 1*1
■
ij Dux Media continue proportionales inter Scmi-Diamctrum & Latus Quadrati injcripti.
i $ Dua Media in eadem proportione continua jnter L. Quad. injcripti > & Latus circum-
Jcripti JeuDiametrum.
ij Dua ex his Media jnter Semi-Diametrum & Diametrum.
16 Proportionalis Media jnter L. Quadrati injcripti L.circumjcripti .
ly Diagramma propofitarum Proportionalium.
iS Series earundem in Diagrammate adnotata (Jf demonjlrata,
ij Detecla tandem reduchonis Peripherie ad lineam reclam } & Tctragonijmi Circuli Oron-
tiana (jr aliorum pjeudographia.
20 VtPeripheria reducatur eyyufct ad Lineam reclam ^ & e contra Mpofitum & nouum
Theorema.
21 Confeclarium ad quadraturam (Jirculi adcommodum.
Senioris non ignore-
tur .
23 Latera quinque regularium (Jcrporum injcriptorum Sphara.
zj Duplicatio Cubi.
Demonjlratio limitum Analoga, Perimetri (Jirculi ad Diametrum.
Demonjlratio Limitum Sinus Smus fcrupuli.
zz Vti Sector quilibet commode quadretur ynodb ratio Perimetri ad Bafim
loannes Mettayer Leitori.
^ X I T tandem ex officina noftra, amice Ledor.Canon Mathematicus,feu ad Triangula, cum Adpcndicibus,& Vniusrr-
falium Infpe&ionum libro. Habebat au&or id confilij,vt vna ederentur Aftronomicarum Infpedionum libri, aufpi-
ciis Chriftianiflimi & auguftiffimi Regis noftri,ad cuius eram Epocha: Syderum adnocatz funt ? Sc fecundum eas eon-
ftruda xjuejLO. Triangula. Sed nouo Se infolito laboris genere deterriti artifices , fculptorcs, fufores, librarij , locarunt
fuas operas difficulter, & locatas praftiterunt ofeitantiffime. Operariorum morofitatem Se focordiam excitabat au-
ctoris prafentia 8e cura,fcd eam homini ad altiora magiflratuum fubfcllia eueeto , Se negotiis pleno,non licuit , quo-
ties res poftulabat,adcommodarc.interca vero non defuere plagiarij , quibus fua ftudia liberiore animo vir candidus
communicarat,aufi ea palam venditare,tanquam fua.Ego certe flagitij indignitate commotus, veritus etiam nequa
in me incideret culpae fufpicio,ca:pi ab au&orc efflagitare, neque,donec conccderct,c6quicui,vt liber is, cuius copiam
licentiofiorcm vitro fecerat, ederetur feftinantcr s quo plagij Sc ftellionatus proderemur rei. T u fac squi & boni,amice
Ledor, ScYalc.
,
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AD CANONE M M ATHEMATICV M,
Liber Singularis.
d Cano n e m , e^r a t h e m a t i c v s^m
ER I AN G VL A,m quafimplieifme cetera omnes plana figura refoluunturpvt f olida in Pyramidas,
Proponitur e^aeSoiVs C A E H 0 L I C A I N S R E C EI ONE
E ERIANGVL1 PLANI
A
FRANCISCI V I E T y£ I, VNIVERSALIVM INSPECTI0NVM
I.
TR 1 AN GV L I P L tA N I RECTANGVLI
Diagramma , Nota.
st N GV LI.
Ls4T E R >A.
C, Perpetua nota anguli
Redi.
B, Acutus a Perpendiculo
fubtenfus.
A B, Perpetua nota Hypotcnufae Redi,
vel Hypotenufge fimpliciter , & jt
i^o^rtv, vtpote anguli nobilioris.
A C, Perpendiculum.
A, Acutus fubtenfus a Bafe.
C B, Bafis.
3
AD CANON EM MATHEMATICVM, LIBER SINGVLAR1S.
II.
LAEERFM TRIANGFLI PLANI RECTANGFLI
TRIMA ET PTTHAGORJ&A
N L O G I *A.
f
I.
ii.
iii.
nil
vt
ad
ita
ad
AB
CB
CB
AB
j* Plus
— Minus
A C
AC
SE V
AB
AC
AC
AB
•j* Plus
'
— Minus
CB
CB
.
< 5 .
A B 'videlicet potcjl AC & C B, ex Pythagoreo imcnt&«
4 FRANCISCI VIET^EI, vniversalivm inspectionvm
III.
CONSECTARIVM, quod ejht
NORMA CANON II.
QJALI v m differentia dimidia inter A B &c A C erit y nitas 3 talium A B miniis vnitate 3 vel A C plus vili-
tate erit quadratum dimidij CB.
vt
CLKL?VltTnUj)$.
r~
Ejlo CB
Quadratum dimidij C B
I oo, ooo
2, 5 00, OOO, ooo
Maior
200 , OOO
10, ooo, ooo, ooo
400, OOO
40, ooo, ooo, ooo
Minorue
50, OOO
6 2 5, ooo, ooo
25, OOO
1 5 (J, 250, ooo
Projlapharcjls
perpetua
I
^Additiua dimidij
C B quadrato,
vt prodeat A B.
Mblatiuaput AC.
AB
AC
2, 500, OOO, OO I
2 / 499 , 999 , 999
I 0, OOO, OOO, OOI
9 , 999 , 999 , 999
40, OOO, ooo, OO I
39 , 999 , 999 , 999 ,
<^25, OOO, OOI
£24, 999, 999
156,250, OOI
15 <6, 249, 999
vcl,fi placet per fwgulas in C B monadas puras , id ejl ,abs fragmentis progredi, ordinata Jeric numerorum
parium
)
L
CB
AC
AB
2
0
2
$
?
4
3
5
&
f
y
8
10
S-
7
7
8
17
Zr
9
9
I O
24
26
&
E S
1 t
12
35
37
L
CB
AC
AB
3
X
3 i "
5
Z
$
7+
: 7
"i
:
9
2.
i 0
21 -
z
II
&
T*
n
13
4 *;
45 ;
1
Jt u redu-
Bionefra
Boru ad
numeros
puros
CB
AC
AB
12
5 =
15
8
I 6T
^ <5
20
21
29
s
- 4 -
28
45
53
8
3 *
77
85
4 - 0
4.0
44
117
125
&
52
\ 6 %
175
AD CANONEM MATHEMATICVM, LIBER SINGVLARIS.
Item per monadas non puras,
I C B
AC
AB
CB
AC
AB
2 2 ~°
IOO
_ 1 1
® 1 00
z~
1 0 0
llO
l 0 0
2 1
* 5 *
221
* J 5'
% 6>
1 100
I-1A
/ IOO
3 —
J 100
3 20
/00
15*
* t *
35*
A-t±
Ti 0 0
x±L
J 1 0 0
e -*- r
5 lOO
feuexre-
duSlione
420
ioo
34 i
* j r
541
i # 1
3 j. 0 0
r
5 I 0 0
7
/ IOO
5 20
1 0 0
5 7*
i $ f
776
z Q
6 ttz
8
J 0 0
10,4-:
<?2Q
8<5"i
I, 061
Differentia prima 1 ry
fecunda '■ ~ ,
& reliqute deinceps augentur r •
CB vero flante perpetuo partium ioo, ooo. detur dius quilibet numerus maior ntinor ue <equabilis ad A B vel A C. Quas ratio erit eequa-
bihs illius numeri ad 2, yoo, ooo, ooo, eadem erit vnitatis ad Proflapkxrefim congruam. & ajr<tnnt\ir , detur qualibet alia Proftapha-
refis vnitate maior, minorue,Vtfe habebit adfumpta Projlapharefis ad vnitatem, ita 2, 500, ooo, 000, ad numerum aequabilem lateribus
AB vel AC congruum , ita quoque 100, 000 ad numerum primum C B. id ejl,ex cuius dimidij quadrato adhibita vnitatis Profla-
pharefigigmtur item primus AB vel A C.
Vt,
r
C B ^ |
perpetuo partium
IOO, 000
Proflaphcerefis
X
Numerus aequabilis
A B vel A C
2, 5 00, 000, 000
Numerus primus
CB
IOO, ooo
Quadratum dimidij C B
ad numerum primum
A B vel A C
2, 500, OOO, OOO
Minor .
I
%
5, OOO, 000, 000
2 0 0 , OOO
10, OOO, ooo, ooo
I
4
10, ooo, ooo, ooo
400, OOO
40, ooo, ooo, ooo
AZrf/o)-.
2
i, 250, ooo, ooo
50, OOO
£25, ooo, ooo
4
6 z q, ooo, ooo
25, 000
156, 250, ooo
AB item & AC ad fumantur Jigillatim partium 100,000. comparantur reliqua latera ad eandem menfuram analoga duce vellam con-
f litata: fenei ,v el ipf orum primorum numerorum triade, ^attque ita feliciter conflruitur Canon , Canonionque lateribus conflans
rationalibus *Atft P eripheria adplicetur,erit ea irrationalis. In Canone yjjf.a rationalis ejl, latera vero irrationalia, veris 'iffcc t.
A iij
6
FRANCISCI V I E T JE I, VNIVERSALIVM INSPECTIONVM
N° B is in conflmclione Canonij es praecipue cura fuit , ifquefcopws , ~Vt in ficmma angulorum acutie res felicius & propius vero , quam forte
per Canonis progrefs tonem liceret , quoties operapretiupt videbitur , examinaretur. Itaque contenti fuimus per f.ngulos C B impares
numeros centum progreai > eojque continua dupla progrefioue Geometrica augere 5 ad metam vfque fex f gurarum , vitra quam tffuja hu-
iufmodi primorum numerorum vajlitas vix ad rem quicquam conducere vifa cft.
Sed proflat fortacis methodum ante oculos proponere.
CB
A B W A C aquabilis
Proflaphctrefs j
JOOy
000
2, 500, OOO, OOO
I
SC^tL^C VKJM^C
Numeri primi
A B
AC
CB
A B w/ A C aequabilis
Projlaph&refts
*
1
25, OOO
100, OOO
0
5 0, 000
50, OOO
i
*
i
5
3
4
100, OOO
25, OOO
I 1
I 1
4 .
17
iq
8
200, OOO
12 , 5 OO
afc &
4-8
8
6 q
* 3
I<?
400, OOO
6, 250
t 9 -
£ S 1
a 6
1,7
zqq
32
800, 000
3 , 125
& deinceps continuata pmgrejiione
t
quadrupla vnitate
dempta vel addita
vfque dum numerus C B fex tam non egredietur figuram.
SC^CL^C SECFN D <yf
3j
I
3
O
O
O
t>
3 3» 3 3 37
1 0
8
150, OOO
1 6,666—
1 7
*■ 7
37
3 S
12
300, OOO
^ > 3 3 3 ?
I 0 8
I 0 8
* i,
*
145
143
24
600, OOO
4, I 66 f
4- ? *•
* J *•
* +
5 77
5 7S
48
I, 2 0 0 , OOO
2, 08 3y
1 , 7 *!
1, 7 i s
+ 3
2, 305
2, 30 3
2 , 40 0 , OOO
I, O4I7
& deinceps , &c. vt s.
t
AD CANONEM MATHEMATICVM, LIBER SINGVLARIS. 7
SC^CL^C CENTESIMA ET POSTI^EM^C
IOO, ooo
2, 500, ooo, ooo
Numeri primi.
AB
AC
CB
A B vel A C aequabilis
92 90 if
9, 899 ^
199
4, 975, ooo
39 ’ *o2,
39 , <500
398
9, 950, ooo
ll S, 8 0 (
1 I 8, 8 0 j
j 9 8
158, 405
158,403
79*
19, 900, ooo
* 7 f>
4 7 J. * x i
796
* 33 > 6*7
^ 33 > *ij
I2 59 2
NO
GO
O
O
O
O
O
i« 900, 8 + 3
* . 500,848
2, 534, 4*3
534 » 4*3
3 >i 8 4 1
79, *oo, OOO
Projlaphcerefis
1 o l
502 - i7 j
2 <1 — -
1 19 9
12 S rd
62
i 99
8 1
3 1 l 99
& deinceps &c, vt s .
SERIE , qua CB adfumitur partium 100 , ooo, ita alfolutd , &*d eam confhtutise regione analogis minimis terminis, non difiimili
compendio ex ijs feries dux reliqux, quarum altera A C, altera A B fimiliter adfumitur partium ioo , ooo , potuerunt comparari. Et
finem quidem, qua AB ejl partium ioo , ooo, omnia retexentes , primo loco praepo fuimus, Dein,qud AC, Tertio, qua C B, vt
idem ordo , tum Canoni , tum Canonio congrueret. Et filius Uteris C B minimos terminos adnotauimm , 'e quibus femifibus qua-
dratis 3 minimi laterum A B , w/ A C, fecundum confeclarij analyftm, futim intelliguntur , adhibita vnitatisproftaphcerefi.
C O N S £ CT ARI 1 R ATIO.
Dum AB conflatur ex numero AC, binario quadratum AB fit <equale quadrato A C, ^ quadrato binarij numeri, &infuper bis
redi angulo binarij numeri in A C, ex elementis Geometricis. nitidem AB /wA? AB A C, docente Pythagora. Quater igitur ad-
fumptum AC, & quaternarius numerus conftituunt quadratum CB. &dscThoy^, cum quadratum CB \ integri ad quadratum
C B dimidtjfehabc.it, vt ratio quadrata 2 ad 1, id ejl , vt ^ ad 1, Semel adfumptum A C & vnitat confiituunt quadratum di-
midij C B.
FRANCISCI VIET^I, VNIVERSALIVM I NSPE CTIQN VM
////.
T %T AN GV L V M FLANVM RECTANGVLVM
C I RCV LO ^DCOMMOV^TVM INSCRIPTIONE,
Circylvs ABC, partium CCCLX cx hypothefi.
Pcripheria AB, Jemi-circulus.
Angvli C Redii amplitudo, Peripheria partium XC. Quadrans circuli , Dimidia AB.
Anguli B acuti amplitudo, Peripheria dimidia A C.
Anguli A reliqui amplitudo, Peripheria dimidia CB.
Anguli videlicet e Peripheria funtjubdupli angulis e centro.
S e m i ssis linea A B,Semi-diamctcr,Semi-fibtenfa circuli, adfumpta partium 100,000 exhypo-
thcfi 3 Sinus anguli C Recti, Sinus Totus.
Scmifsislinea AC, Semi- latus, Semi- ve fubtenfa Polygoni duplata peripheria amplitudinis B in-
icripti, Sinus anguli B acuti.
Scmifsis linea C B, Semi-latus , Semi- ve fubtenfa Polygoni duplata peripheria amplitudins A in-
fcriptijSinus anguli A reliqui e Redto.
V. TRI AN GVLVM
i
- — • - • — • ■ - ■ ■ ■ -- - - - . ... _
AD CANONEM MATHEMATICVM, LIBER SING VLARIS.
K
T A N G V LV M PLANVM %E CT AN GV LV M
CIRCVLO ^fDCOMMOV^fTVM CIRCVMSCRiPTIONE,
PERPENDICVLVM
Angvlt B acuti amplitudo, Peripheria C y.
Anguli A reliqui e Redo amplitudojRefidua C y e quadrante amplitudine perpetua Redi C.
CB, Semidiameter, vt Sinus Redi in Triangulo inferipto.
A C, Semilatus Polygoni duplata Peripheria amplitudinis B circulo circum feripti , in iis partibus,
qualium Semilatus Polygoni duplata peripheria Refidua circumfcripti, Semidiameter.
AB, Hypotenufa analoga.
h R EV E Sinus vocabulum, cum jit artes, Saracenis pr&jevtim quam familiare ,non ejl ah artificibus explodendum ^ad latentm femifium in-
f 'criptarum denotationem. Utera vero circum fcripta,neutiquam inter fe confldtiafed vaga & ita Diametro adfixa, vt ah ed perpetuo hi
Jecentnr cpjtxa , & edttcla a centro Circuli Hypotenufa magnitudinem eorum concludit , non jortita ftnt haSlenw nomen elco-as
Sed quoniam Raphjodijuos Cdnonas,m quos ea congejfernnt , Factmdos vocaucre, femifia Jane huiufmodi Latera vocentur Facundi vi-
delicet Sinus, N imerive & eorum h lyp o t c nuf<£ , Hyp o t cn ufe Facundorum ,ne fucus forte fat , <& muitate verborum res adumbretur.
B
IO FRANCISCI VIET^EI, VNI VERS ALIVM INSPECTtONVM
V I.
c/iD STNTAXIM LATERVM IN SC RIPTO RFM,
KYPIil' TEPA GEOMETRICA
bojiulata.
f
1 S E ivi i-d iameter, RadiusVe Circuli^la-tus eft infcripti Exagoni.
Latus infcripti Tetragoni poteft duplum circularis Radij.
Latus infcripti Trigoni poteft triplum.
Latus infcripti Decagoni, produdtum femifte latere Exagoni, poteft Radij fefqui-akerum.
Latus infcripti Pentagoni poteft Radium.plus latere Decagoni.
Ite m,
2 Sinvs Reftdue poteft Sinum Totum,miniisfinu Peripherie.
Item,
3 S i n y s Verfus Peripherie (eft autem Sintis Totus , minus finu Reftdue) dueftus in Totum, id eft,
adie&is quinque numeralibus circulis, eft Duplum quadratum finus dimidie.
&ceu'ct'WAir, Duplum quadratum finus Peripherie diuifuma Toto, id eft , abie&is quinque
numeralibus circulis, eft finus V erfus duple.
a
Item,
4 Svetensa Peripherie, qua differunt due, poteft Hyperochem finuum Duarum , & Hypero-
chem firmum Refiduarum.
Xnde C°N SECT^iKIV M.
Differe nti^i inter finus aqm di flantium Peripheriarum,a LX. tanta eft quantus finus
dimidia Peripher:a,qud dijflerunt inter fe 0 id eft , integra qua abfunt dLX.
Et ideo, c D^t is Sinubus ad partes X X X. dantur Sinus reliqui fold oAdditionis , vel
Subductionis via .
AD CANONEM M ATH EM ATI C VM, LIBER SINGVL ARIS.
ii
VII.
sAD S T NT AXI M LATERVM CIRCVM SCRIPTO RV M,
KYpm'TEPA GEOMETRICA
*
poflulata.
%
i Ansylvs Trianguli aequilateri valet duas tertias redii.
% Hypotenvsa & Facundus Refidux periphcriae aggregata, funt FaecundusPveliduae fcmi-
periphcriae.
& Facundus Reftduae peripheriae , eft Faecundus & Hypotenufa refidui Duplae
peripheriae.
3 ' Differentia inter Faecundum &c HypotcnufamRefidua; , eft FxcundusDimidix peri-
pheriae.
& ow&VcDUi/, Faecundus Peripheriae, eft Differentia inter Faecundum &: Hypotenufam refi-
dui Duplae.
Ex his CONSECTARI VM,
J).atis Facundis ad partes XLH. dantur Facundi reliqui , CE) Facundorum Hypo-
tenufa omnes O fola aAdditionis 3 vel Suhducfionis vid.
i? E s I D v a peripherid, Refiduum periphcYU^BdfisTomptimenttm fcu Tl<tpy.‘7r\i\pa)pM . , funtfynonymd.
vAEcfuefynonyma, Sima fecundus Peripherie , Sinus bafios Peripherie , Sinus Rtjidue pcriphmte , Sinus
reft dui, co mplem en ti fu dzfjeyriw A pueTai Peripherie.
, r\ _
\ /
/
12 ♦ FRANCISCI VIETA^ VNIVERSALIVM INSPECTIONVM
DIAGRAMMATA
A D APODIXI M GEOMETRICO RVM POSTVLATORV M,
A D f m & 2. Km
infcriptorum.
Vide apud Ptolem.
cap.y.li.L
A d 5 um infer L
ptorum-
A N a L Y ticom Trian-
gulorum Syntaxeos pri-
mum 5 infra' vbi
vide.
■w
AD CANONEM MATHEMATICVM, LIBER SINGVLARIS.
13
d 4'™ inferi-
p torum.
iA d 3 !1
circumfcri -
ptorum.
A y, & B yfu/t periphc-
ria.
^4 N A L Y ticoru T r Un-
gulorum fecundum ,
Analogia Archimede a.
vt
ad
ita
ad
AB
CBi AM
MC
&: perfynaerefin.
AB
CB
AM
MC
t
t
CB
MC
id (fi-,
AC
AB
t
CB
&:per interpretationem, &
AC
AC
AB
CB
CB CM
Terti vM .Tnaly ticum T r i umidum.
o
S v n T & poflulata n^oAtmre^t. Triangulorum paffim fubaudienda,& fupplen da, qualia funt haec.
I. Trianguli tres angulos aequales effe Redis.
II. Duo quaelibet latera maiora e(Te reliquo.
iii. Maiorem angulum a maiore latere fubtendi,
mi. Asquiangula cruribus effe proportionalia.
B iij
(
FRANCISCI VIET yE I, VNIVERSALIVM INSPECTIONVM
VIII.
RVKSVS ^4 D S T NT A X 1 M,
MM BITI 0 STB LINEjE AD RECTAM ANALOGIA
per plus ^ minus.
® '
TERMINI
ANALOGI.
I.
II.
m.
mi.
Pcripheria
maior.
Pcripheria
minor.
Sinus Peripherie
maio is partium
tot accvrate',
vel, & ampliv's.
Sinus Peripherie
minoris partium
tot mu!to magis
& A M PLl v's.
Periphcria
minor.
Pcripheria
maior.
SinusPeripherice
minoris partium
tot accvrate',
vel,P £ r £ v .
SinusPcripherie
maioris partium
tot multo magis
PER e' 1 .
ANALOGIA GENEKALIOK
in numeris irrationalibus.
Numerus
Numerus
Numerus
Numerus
fere'.
accvrate'.
accvrate'.
[
ET AMPLIAS.
Numems fere', id ejl, dum excedit iujhm }
ET ampli v's .fittm deficit d iufio.
AD CANONEM M ATHEMATICVM, LIBER SINGVLARIS.
IX.
oAN ALO G IA tandem TERIMEL RI
CIRCVLI MV VI^METRVM.
Minor vera.
Qvalivm Semi- Diameter
ioOj ooQj Oo °’ 00 accurate
Talium Scmi-Perimeter Circuli,
314, 1 & amplius*
Maior vera.
100, ooOj Qoo. 00 accurate.
Media fatis accurate.
IOO, OOP, 0oa -
159, igf, j 7 fere.
314 , 1 59,
SINES VNIVS SCREPELt.
Minor vero.
ogg, 31, s>s -9 & amplius.
Maior vero.
2-9, ° 88 ’ g*. fere,
■rsr
Medius fatis accurate .
A
^ o 8 8, 81, 04.fr
•846, '<■ »» «Mj
/.
84 ^,
f , 94., 8 1. o <J
84 ^, -
r, 94-. 7?. ? *■
RELI QV I Sintus, reliquave latera, tota vel femifiia,infcripta fiu e circum fcripta,ad (jtt&uU etiam Polygona, integra ve!
dimidia, hts vejligiis brorfus Pythagorias, ,4rchimed#is,& Ptolemaicis non infeliciter comparantur. Et conjlituitur in Canone vere
Mathematico, & Mathefeos Thefouro, TRIMN GV LI PLMNl RE C T M N GV LI,&c. vtpag.fequ.
V
Et cum Hypotenufa in prima Jerie peculiare nomen fortiaturjntelligantur fne i
velfimplici Hypotettufc nomine } HypotenuJce F acundorum-
Contentvs autem Canon efi centenario millenario numero ai taxatione Semidiametri Totius infcripti. ; xx a J r v
fi ma partium c cclx. Circuli aptare, quod vlterius progredi ft otio fun ----- ■' ~ ■>
FRANCrSCI VIET,®!,
VNIVERS ALIVM
tnspection VM •
X
TRIANGFLI
PLANI RECTANGFLI
M D C I R C V L
V M M D C O M M O
D M T I
infcriptione, circumfcriptioneue y S ebjes <j
feriei Analoga, pro numero Laterum ,
vel aAngulomm.
c Rectus.
Acutus.
Lfeliqum,
A N G V L I.
C.
• B.
A.
Latera.
AB.
AC.
CB.
Hypotenufa.
Perpendiculum .
Bajis.
I.
\
Sinus Rc£li, Sinus Peripherie
Totus, Hypotheticus.
Semidiameter.
Sinus Refidue
II.
Hypotenufa F^cun
di Peripherie
Faecundus
Peripherie
Totus.
III.
Hypotenufa Facun-
di Refidu e
Totus.
Faecundus
Refidue
Ingula Sexa-
Fr agmentorum enim
. A. Arcuu apta} e quoa vlterius progredi Jit ea ... Urm omnino & oneret non tuuei Mathematicas fcientix fludiofos
ope quando vfmpojlukt [poflulat autem, r ■ , : comparabuntur , vel adfcmunciam fere vnim fcmpuli, numeri
AD CANONEM M AT H EM ATI C V M, LIBER SINGVLARIS.
'7
congrui, cum hadlenus ex canonibus Sinuum, qui videbantur accuratiores, nec ad prupulum quidem accurate poterant dari, sit in Canonis
noud conJlru 5 lione,ea curafuit,vt inter duos proximi fequentes numeros non minor effet differentia , quam aliquot particularum viginti ,
& ea tenus fra Bion es adhiberentur, alioqui negleBce. Quod enim continuantur in ferie Hypotenufa fupra vicenarij numeri metam , id efto
Jane , vt comitentur fragmenta bafeos prima ; Jeriei.Iuuat enim interdum collatio , atque adeo forma redditur elegantior .C<eterum cum trzrt-
| 3 o.M,ct ad fecunda fcrupula non poffunt accurate accipi, vt accidit interdum in fammd angulorum acutie, commade fupplet Canonion. Quod
alij tentabantfuorum Canonum ad fcrupulorum dextantes porreclione. Sed infeliciter & knyycci , dum vaitos numeros , & immenfos,
vel d tribus quatuo'rue primis figuris Jaljds,&falfb enunciatospro veris inducunt factos yideheet a minimis irrationalibus , cum potius
minimi irrationales d maximis gigni debuerant. Neque enimfi numerus 29 eft Sinus vnius fer upuli, qualium Totus 100,000, ergo, qua -
lium T secundus vnius fcrupuli erit vt Totus, talium numerus , qui prodibit ex operatione sinalogicd , erit Hypotenuft facundi. Jmmo
p r<z ter a Itera m , tertiam 'u e Hypotenujk figuram falfa funt reliquse omnes, & fi circuli adderentur, tam effet accurata , acfortaffe etiam ac-
curatior,quam cum fuis adferiptis efalfa diuifione numeris. Ejl enim numerus 7.9, Sinus quidem vnius fcrupuli ,fed iyyv$u,no accuratus.
Et vt duarum figurarum efl duntaxat , ita numerum nullum fiiprd duas figuras efficiet accuratum. In quem tamen elenchum Rhapfodi
incidere omnes , quibus oportuerat potius Mrchimedad via progredi, & filias d matre, non d matribus f lias deducere. Numeri autem Cano-
nici ideo per ternas di ftingunturfi guras, ne immenfitas txdio jit,& aciem oculorum, cui confulcndum ejl, offendat. Hac diftinSiionum co-
moditate non freti folertes alioqui Logifhz, magis probabant in Canonum JlruBuris ad Triangula, vti panium Sexagefimis, Sexagenis,
adfumpto Sinu Hypothetico partium 6o,feu vnius Sexagena. Mtfafi proflo fit tabula faxofadm , vix multiplicant, vix diuiduntyvix e
quadratis Utera extrahunt Jecure. Omnino lubrica efl huiufmodi Logifiice, in quam negociofum ejl non impingere. Neque in ed , erf
Mftronomicam vocant, vlla inejl methodus, qua non ft in Catholica paratior, & expeditior. Quod enim in circulationibus, per Sexagefima
pra flant, & Sexagenas , adfxo circa tabella, no ' fine fafiidio lafione oculorum , intuitu, idem per partium Millefima,& Millenas prom-
ptius abf oluit ur , & felicius, abfque vilius tabula inJj>cBione,ex Jold communi Mritkmetices vid. Denique in Alathematicis,Sexagcfimo~
rum& Sexagenarum parcus vel nullus, Millefimorum vero & Millenarum, Centefi morum & Centenarum, Decimorum & Denarum,
& iflitis generis vere Mrithmeticc rum adfcenfuum & defcenjuum ffreques vel omnis, vfus cfo.Siibiecla tamen eft pojl Mathematicum
Canone & Cdnonion,ipfia , ne quid defleretur Jfaiofahiv tabell a, quam alia mox fcq uitur, f ractionvm apud Mathema-
ticos vfi tatarum, alterius in alteram reductionibus adeommoda. canonios denique T ridvilorum ad fingulas partes quadrantis cir-
culi, fecundum xoyfaBov LcgiJlicem.Iam fequuntur r^r d.vcLyuQoi.Acucioiv inspectione
XI. CANONICjE
FRANCISCI VIETAEI, VNI V ERS ALIVM INSP ECTIONVM
XI.
CANON ICAE IN TRIANGFLO PLANO RECTANGFLO
MN.ALOGIME S E X LxITERVM ET M N GV LO RV M CVM SINV
ILe£ti,Jeu Hypothetico .e x qv / b v scatis prater angulum re-
cium 5 latere tf) angulo, <vel lateribus duobus ,
datur TRI alN GV LV M.
Sinus Redii ,feu
Hypotheticus
Latvs
Sinus Acuti
Latvs 1
I.
C
AB
A
CB
II.
c
AB
B
AC
Sinus Hypotheticus
Acuti., vt Redi
Latvs
Hypotenufa
Latvs
IIL
G
CB
B
AB
IIII.
C
A C
A
AB
Sinus Hypotheticus
Acuti, vtRedi
Latvs
Facundus
Latvs
v ;
C
CB
B
AC
VI.
C
AC
A
CB
©
Quod praejiant dux, intermedia, id duabus prioribus potuit abfolui,nififortajfe commodior Multiplicationis quam Diuifionis via.
Vbi Xero Mnguli duntaxat dantur, fatis ex fuperioribus intcllipdtur dari laterum rationem,adfmptis e Canonis vtrdlibet ferie numeris
congruis, ex prima dum Simus Totus adfgnatur Hypotenufx,ex fecunda dum bafi,ex tertia dum perpendiculo.
AD CANONEM MATHEMATICVM, LIBER SINGVLARIS.
39
XI L
X N 1 10 G I JE TOTIDEM
Mbs Sim c Rectu
Sinus
Latvs
Sinus
Latvs
I.
A
C B
B
AC
Fsecundus
Latvs
Sinus
Latvs
II.
A
AB
A
AC
1 1 1 .
B
AB
B
CB
Hypoccnufa
Latvs
Facundus
La tvs
1 1 1 1 .
B
AB
B
AC
y.
A
AB
A
CB
Hypocenufa
Latvs
Hypotennfa
Latvs
y l
A
CB
B
AC
\
C ij
zo
FRANCI SCI V X E T JE X, VNIVERSALIVM INSPECTXON VM
XIII.
zAD STNTAXEOS N 0 R M A M Jn Analjfi, TRIAN GVLA
P L N yC J^E C T N G V L T \1 ^T, DISPOSITIS , y T DEINCEPS P E E^P E T V o''
obferuabitur , noua & analoga methodo terminis.
f
m MV M.
Sinus Redi,
Totys.
AB
Subtenfa
Peripherix
integrx.
Sinus
dimidix.
CB
Sinus Verfus
integrx.
B
AC
Sinus Refidux Sinus Peri-
dimidix. pherix inte-
g r ^
ReBmgulum C in C B aquale Re B angulo A in A B ,id ejl , duplo quadrato Sinus dimidia. Quod pertinet ad f m pojlulaitm
inferiptorum.
SECVNDVM .
Sinus Redi,
Totys»
AB
Subtenfa Peri-
pherix, qua dif-
ferunt dux.
A CB
Sinus dimidix Hyperoche
cius , qux fit e finuum Refi-
duabusaggre- duarum,
gatis.
B
AC
Sinus Refidui di- Hyperocbe
na id i x eius , qux Sinuum
fit ex duabus ag- duarum,
gregatis.
si dux Peripherie? aquidijlanta LX, in contrarias videlicet partes, aggregata femper erunt V !**■ Dimidium aggregatarum L X, angu-
lus h.& bimulus B XXX, citius ftnus 50,000 dimidius C .Ergo A C dimidius A B. Ejl autem A B fimis duplus differentia dimi-
dix duarum, fit integrx,quaabfwtk LX.& ideo KCfmpltis. Quod pertinet ad 4.™ pojlulatum inferiptorum, & ad CanfeBmum.
AD CANONEM M ATHEM ATI CVM, LIBER SINGVLARIS.
11
TERTI V M.
C 1
AB
A
CB
B
AC
T o tvs.
Hypotenufa
Sinus
Totvs.
Sinus
F&cundus
Hypotenufa
Peripherie.
Refiduae.
iff per Synthsfinu,
Peripherie.
Peripheriae.
Hypotenufa
Fafcundus
Totvs.
Totvs.
Faecundus
Refidue.
Peripherie.
Refiduae.
Jiem per Sy nthefwu.
Peripherie-
T OTVS.
Hypotenufa
Refiduae,
Smus
Refiduae.
Farcundus
Refiduae.
Sinus
Peripherie.
T otvs,-
C
Totvs,
Vel, propter ^Analogiam <tA rchi med&arru.
BM
Hypotenufa
Refiduae
dimidiae.
M
CB
Sinus Hypotenufa &;
Refiduaedi- F.rcundns Re-
midia:. fiduac integrae
aggregata j feu
FiECVNDVS
dimidiae Refi-
duae.
^ ANALOGIA cA \C HI MED M A.
B
Sinus
Peripherie
dimidie.
* V ndefi CBfit Totus
ficut A C, erit C M fi-
cut AB minus CB.
Quod pertinet adpoflu -
latum tivctmfcri -
p torum.
Fecundo Refiduae.
CM
Totvs.
AB
CB
AC
CM
t
CB
Hypotenufa Peri-
Totvs. t
Facundus
Faecundus
pheriae integrae,
plus Toto.
integra.
dimidiae.
vel,
Hypotenufa Refi-
duae,plus Faecun-
do Refidu 32 .
Faecundus
Reddiuc.
Totvs.
Diefis *
Totius*
AC
AB
'k
CB
Tot v s.
Hypotenufa Refxdux, minus
* Vnde ,ft C M
fit Totus ficut
AC, erit CB fi-
cut A B plus
C B. Quod perti-
net adpofuUtam
z’ ,m circumfcripto-
ntm.
zz
FRAN CISCI VIET^I VNIVERS ALIVM INSPECTIONVM
C
Totvs
%-A N A LO G I A E j. Triangulo
per DUrefim interpretationemjiegocio bene adcommo
AB
Sinus duplus
Peripherie,
£ N ij . Triangulo
C
Totvs.
c 4LIA
A
ALIA
B
C minus B
Verfus Peripherie.
A B minus A C
ExceiTus finus dupli,
fiupra linum
duplat.
^ A
CB
_Sinus fimplus.
Verfus duplat.
ojtnjidereefijeclo.
f A
CB
| Sinus Peripherie.
L_
Exceflits Hypotenufie
Peripherie fupra
linum Refiduar,
1 B
AC
^.Sinus Refiduar.
Sinus Peripherie.
Diagrammate.
o
r B
|
AC-
[ Sinus Refiduar.
Semidiameter.
) AD
I Sinus duplus Rcfi~
L due.
AC
Diameter,
Conjectarium infignz. *>.
Latus quadrati circulo infcripti eft proportionale inter Hypotenulam Peripherie, &finum duplum Refiduar.
Quippe latus quadrati potefl duplum Semidiametri , quod ejl , 'faBum Semidiametri in Diametrum .
AD CANONEM M ATHEM ATICVM, LIBER SINGVLARIS.
XIIII.
TRI ANGVLVM TLzANVM OJBLl QVAN GVLVM.
A. T1
^Anguli. Latera.
A,
Angulus verticis.
BD,
Bafis.
B,
Angulus ad bafim liniftcr.
AD,
Crus dextrum.
D,
Angulus ad bafim dexter.
AB,
Crus finiftrum.
Plana obliquangula diducuntur in duo Re dlangula, eduElo perpendiculo ab angulo verticis ad bafim. Ita vero feciio injlit nenda ejlgvt
e tribus datu terminu {tot enim exiguntur)duorttm faltem non offendatur notitia.
TBRMINI PLANI 0 B Ll Qjs AN GVLl
SERIE ANALOGA.
Sinus
Latvs
Sinus
Lat vs
Sinus
Latvs
A
BD
B
AD
D
AB
Ex infcriptione Trianguli in Circulo.
Meminiffe autem oportet in obtujdngulo obliquangula Anguli obtufi amplitudinem,' vt exterioris y non interioris, a Latere Jkbtendi, cum
fu Diameter maxima infcriptarum.
24
FRANCISCI VIET vEI, VNIVERSALIVM I NSPE CTION VM
XV.
P ARASCEVxE <ad sectiones obli qvangvlorfm.
i. Dum ex Lateribus exquiruntur Anguli.
AD poteft AB & BD, minus BD in CB bis.
I g it v R in Triangulo obliquangulo A B D datorum laterum, educlo perpendiculo ab A verticis angulo ad B D bafim.
Si a potentiis AB cruris fini ftri,& B D bafeos aggregatis, auferatur potentia cruris dextri A D, & reliqui dimi-
dium dtuidatur per B D bafim, prodibit C B,Quod erit, vel bafeos Tegmentum finiftrum,fiminusbafi,vel,fi maius,
baris ipfa in dextram protraria, fecundum anguli ad bafim dextri adfectionem, quo nempe acuto caditperpendi-
culum intra, obtufo extra Triangulum.
A 7Tdhl£l$.
Dum perpendiculum cudit intra T ri angulum, BDwCB bis.xauale ejl C B bis in je,& C D bis in C B ficuti 7 in 4 ttcjuale efl ^ in j\.,&
y.n 4. Mt AD potejl AC & C D . A B vero potejl ACc^CB.BO item potejl CB^CDjCjtCD/»CB bis. Auferatur
igitur potentia A C & C D a potentiis A B & B D , remanebit C Bbu in fi, & C D in C B bis.
Dum perpendiculum cadit extra, B D in C B bis,#cjuale ejl B D bis in fe,& B D in C D bis. Mt AD potejl A C ^ C D. AB vero potejl
AC CB.Et illud CB potejl CD,*^ B D,^ bis B D in C D.T antepotenti# A B adiungatur potentia B D ab aggregato de-
matur potentia AC^C D, remanebit B D bis in fi,& B D in C D bis.
P OTV I T idipfum aliter enunciari , nec dfiimili via demonjlrari.
A B poteft A D &c B D, minus B D in C D bis.
Ite m, ex additionum & fubduElionum regulis ,
A B poteft A D, miniis B D.plus B D in C B bis. hei ,
A D poteft A B, miniis B D, plus B D in C D bis.
TERMINI AlNMLOG^l SERIE.
I.
Balis.
11 .
Dimidia Potens crus
dextrum & bafim, mi-
nuscrure finiftro.
VEL,
Bafs.
Dimidia Potens crus
finiftrum & baf m, mi-
nus crure dextro.
m.
Dimidia Potens qrus
dextrum & bafim, mi-
nus crure fimftro.
Dimidia Potens crus
finiftrum & bafim, mi-
nus crure dextro.
////.
Bafeos a perpediculari Teg-
mentum cruri fniftro con-
terminum, vel ipfa Baftsin
dextram protra&a.
Bafeos a perpendiculari feg-
mentum cruri dextro con-
terminum , vel ipfa Bafisin
finiftram protradta.
-A
Aliter, Parafcme
1
AD CANONEM M ATHEM ATIC VM, LIBER SINGVLARIS.
33
Aliter fP arafceue ex lateribus exquiruntur anguli .
Factvm b e in B y aequatur
fado BD in B £.
P I g i t v r in Triangulo obliquangulo A B D
datorum laterum, edudo perpendiculo ab A,
vt verticis angulo ad BD balim,
Addatur AB crus AD cruri,
Ducatur B E aggregatum, in B y excefium lon-
gioris, Fadum illud (cui aquatur B D in B £ )
diuidatur perB D Bafim .Inter B £quocietem,
& B D bafim, D C differentia dimidia, erit B D
bafeos ab edudo A C perpendiculo contradio,
protradiove. Contradio, fi bafis quotiente
maior, Protradio, fi quotiens bafi, Secun-
dum anguli a bafi & crure breuiore comprehefi
adfedionem,quo nempe acuto cadit perpendi-
culum intra, obtufo extra Triangulum.
Ex elementis Euclid<eis Prop.$6.lib.vj.
TERMINI ^4N MLOGM SERIE.
I. II.
Bafis- Differentia
crurum,
B D B y
III. IUI.
Crura ag- Bafis contrada,vel produ-
gregata. da dupla contradione, vel pro-
dudione ad eam, qua contrahe-
retur, vel produceretur a perpendiculo.
B g B £
DEINCEPS
IV Crusbreuius. Bafeos contradio,
ycl produdioaper
pendiculo.
AC « CDfceuCC
^EN^TLOGI^E.
Sinus Sinus complementi anguli
Redi. a crure breuiore, & baficom-
prehenfi,interioris,extcrionsve.
C c A d feu C A c
z» Crus longius. Bafis cotrada, vel pro-
duda a perpendiculo.
AB AC
Sinus Redi. Sinus complemeti anguli a cru-
re longiore, & bafi comprehefi.
C \\' bAc
j. Anceps Obliquangulum .
P l an e v , Datis cruribus & anguloru ad Bafim altero, duo in qua; fecatur obliquangulum, dabuntur triangula redan-
gula. At ipfum obliquangulum anceps efb. Anceps quippe bafis.contrada vel produda a perpendiculo, anceps
angulus perpendiculi, contradus velprodudus, anceps denique angulus reliquusad bafim, exterior vel inte-
rior. At horum altero conflituto,confHtuitur confentanee totum Triangulum. Vt, inaltera figurarum, Datis A B,
& latere quod fit longitudinis AD , quantum, e fl etiam A£, cum angulo B, Dabuntur Triangula reflangula ACB, ^ ACD,
sui aequale Ac ^it ipfum obliquangulum erit A B D, vel A B £. Vbi vero definierimus anguli ad bafim reliqui adfeSlionem , in-
teriorem videlicet eum ejfe , vel exteriorem , acutum vel obtufum, definiemus congrue reliquos quoque terminos. Et huc pertinet Pro -
pofiji lib.j. Triang. Regiomofft .
D
54x6: FRANCISCI VIETaEl, VNIVERSALIVM INSPECTIONVM
IN 0 E LI QV A N G VLIS SECTIS
in Obliquangula frequens Parafceue .
/.
//.
Latus fccans
angulum.
Segmentum late-
ris angulum fe_
dum fubten-
dentis vnum.
Ex dementis Euclideeis,
III.
enti
alterum»
Segmentum
IUI.
Lateris fequentis
produdio ad peri-
pheria vique Cir-
culi triangulum
circumfcribentis.
probo 5 .lib.iij .
Poiro, inbife&Ione D anguli, duplum D G lateris fecantisfemperminus efl: cruribus A D & B D aggregatis. Quod
apud ^irchimed, demonjlrat Command.lib.De lineis Spiralib .propojit.iy
j. I N Ad IS C E LL qA N EIS denique P L A N 0 R V AI
SELECTIO RES ^ iLIQVOT ^4 N ^4 LOGI ~4E y C PRIMV^M^
EI A I K n T E P AI.
IN RECT^EN GELO ,E D ECT^ B ANGELO RJECTO R E RREN D 1 C EE^ERJ.
I.
i Hypotenufa.
A B
u.
Perpendicu-
lum, vel Ba-
fis.
5 ' ^ B.
n Hypotenufxa
Perpendicu-
lari fegmen-
Perpendicu-
laris.
tum vnum.
A C
GC
iii Hypotenufa.
Latus vnum
circa redum.
A B
GB
A G
AG
ui.
Bafis, vel Per-
pendiculum.
AG
mi.
Perpendicularis
ab angulo Re-
do eduda.
cm.
B
Perpendicula-
ris.
GC
Hypotenufae fe-
gmentum alte-
rum.
CB
Latus idem.
Hypotenufx a
Perpendiculari
fegmentum lateri conterminum.
GB
CB
AG
A C
C AGB ?
S v n t enim cequi-angula < A C G 5* & ideo lateribus homologa.
CGC
AD CANONEM M ATHEM ATI CVM, LIBER SINGVLARIS.
2 /
f- IN OBTFSANGFLO OB L I Q_F A N G F L O E V F C T A A F E RJT ICE
Perpendiculari^ duabus ei Parallelis 3 djingulo videlicet crure Jinguld, inaequalis altitudinis fub aquali Bafi.
Differentia Alti- Altitudo minor,
tudinum inter
Parallelas.
OfJL
fiv
Bafis obliquan- Bafis produdio- j
guli, feu Differcn nis obliquaguli, |
tia bafeam duo- feu redanguli
rum,in quae fcca- minoris.
tur,redaguloru.
B D D C
B f
D V
Ejl enim BD^DQ vt A <p adtp C: o /xvero ad pv ejl,vt A <p d,dq C .Nam Do ad ov ejl, vtD A ad AC: & D fj, ad y. y vt j
D <p ad <p C:& Do ad DA vtDju,a D c p. Vnde o j ad ^ y ejl vt A C ad <p C. Ergo vt o v minus n y,id ejl 0 ad ^ v, ita A C
minus q> C 3 idejl A <p,ad <p C.
iij. IN O B T F S A N G p L O O B L l Q^F A N G V L O, E E> F C T A A F E RT ICE
Ferpendiculari } & duabus £r Parallelis , a Jingult delicet cmre Jinguld aqualis Altitudinis fub inaquali Baji,
Differenti a ba- Bafis longior fub
fe<yn,fub quibus qua elata efl al-
elatae funtParal- tera Parallela-
leLs. rum.
B o Bg
Item
Altitudo Paral-
lelarum.
vg
Bafis obliquan- Bafis obliquan-
\a guli/eu Differe- guli produdi,
tia bafeom duo- feu redanguli
rum, in quae feca- maioris,
tur, redaguloru.
BD BC
Altitudo trian-
»
AC
guli.
O £ D i C
Ejl enim B £ ad B C, vt v £ ad A C: & v £ ad A C, vt D T feu 0 ?,ad D C: & ideo vt B £ minus 0 £,id ejl B 0 ,ad B ita B C minh
D C, id ejl BD, adBC.
ittj. IN R^ECTANGFLO, FEL O B L I Qjg A N G F L O, INTIBA Q_F 0 D
defcnbttur Quadratum.
Bafis, & altitudo Bafis.
Trianguli,
aggregata.
A fJL
ecqualis
AC & BD
aggregatis
XfJt,
aqualis
BD
Latus quadra-
ti triangulo in-
fcripti.
EC
Ex conjlmSlione A E ad E C, e]l,vt A C ad B D, & permutando AC ad A E, vtB D adBC. Jit vt AC ad AB, ita AD ad
A G, Ita etiam B D ad <p y. Ejl igitur <p y eadem qu<e E C.
/ . //,
rr/ . ////
/te .
////.
D ij
'M- ytf=. xA-Szjc / 4 - w ////
/fc.Jt. 'Btt.Xc. \>A-Ac. ,A% yx.&c .
AC ■ X. JA> .Jy ■ Sq. :b:d
‘C/ /// ////
A'
'iiZK
JL-
/
N \
■ "
/
A-
x ' B
1
D- W.
x \
^
, jJ c . JJAA At T> ■ tp a - ix.s(o :
f !.//■//(■
A D.A Cj<- a V - ai. ac- TD.
V G-dt At>- Ai- tv- Jt>abc.
. JIO-AI-AC- jt$. *£..£$ -A. X S .
A I . #L. £tt / A v • Jf r - P B ,;, J " 1 • ' £ *x° ■
7nc. a ■ rv y Ab ■ Ai- T cy-BV . A"J Ar igf ■
. . -4 -t T 1 < /7
tt i Cfon-uj . ./?. ^ 4
ly. 't fry ■
E Ecro • B - A I $ C ' l T”
-ua A'’
i txA —
28
FRANCISCI V I E T iE I, VNIVERS ALIVM INSPECTIONVM
V.
INI QFADXJSECTO A DFABFS DI AMETEJS CIKJCFLO.
\
Fa&um & S' in & sequatur Fa-
potentiee lateris Qmdrati Circulo inferi -
e*, do ctv in do, «m» vtrumque aequetur
ptjvt oflenfum ejlfiupra.
& ideo fmt Analogi Termini.
et <b
/
Lateris edudi ab angulo
S emi- circuli fegmentum
a Diametro diagonia.
Ct V
II
Segmentum Lateris fe-
cundi.
CtO
ni
Latus fecundum.
CL&
llll
Latus primum.
NEC male ita enunciabitur Theorema. Si reda: inferibantur in Circulo, ab eodem Peripherie pundo,vna cum Diametro
& fecentur ab altera Diametro diagonia,RedaguIa contenta fub tota,& fegmento ei pundo e quo educuntur conter-
mino/unc aequalia.
SED neque fmt omittenda ex eodem Viagrmmatehue non pauca vtilitatis Analogia.
I et fi quadr.
II a, fi quadr.
III a j\ quadr.
fi quadr.
ct, L quadr.
0JN quadr.
a. | femis.
et fi
(0
a, fi femis.
:a>
AD Demon finitionem i *,Ft quadratum & e ad quadr. g f ita clP ad Z cc,cum jit g ^ proportionalis media inter o.fitF At et fi ad fi ^ efi m ea ra-
tione, qua cL^ad .Ad z am Ft quadr ■ of ad quadr. ita a. fi ad et», cum fit ace proportionalis inter & £ CT ct a ■ At eadem efi ratio
ad ,x t,qua ct (i ad ct <L Item ratio ctfi^ad ctea eadem qua femis ad dimidium ct u, id efi, ct fi.
Tertia efi Synrhefis e prima, Ft ct (i quadratum plus fi L quadrato, id efi, & P' quadrat, ad fiP quadrat. Ita ct^plus ^ oo,idefi ctan^d^ «. Ita igitur quoque
et 00 fimis, id efi ctfi><td fi a fimis.
rENNlKflTEPAl.
LN LIFE A SECTA.
Dimidia potens lineam minus vtro- Segmentum vnum.
que fegmento feparatim.
Segmentum alterum.
Potens dimidiam, minus differentia Diefis (c£tx
inter dimidia, & fecus feds quam
bifariam, Diefim vel Apotomen.
Item.
Dimidia potens lineam, minus
feparatim vtroque fegmento.
Apotome fed^.
Tota,
Potens dimidiam, minus diffe-
rentia inter dimidiam & fe-
cus fedtas quam bifaria, Die-
lim vel Apotomen.
IN LINEA SECTA MEDIA ET EXTEJSMA ELATIONE.
Maius fegtnentUjid eft,exce(Tus,
Tota continuata maiore fegmeto
quo Potens totam & dimidia,
feparatim, fuperat dimidiam.
Tota,
Maius fegmentum.
Tota.
Minus fegmentum.
Maius fegmentum.
/
AD CANONEM M ATHEM ATI CVM, LIBER SINGVLARIS.
Tota continuata minore
{egmento.
Minus Tegmentum,
Minus Tegmentum.
Maius Tegmentum .
Item ,
Item,
Tota,
Differentia Tegmen’
torum.
Linea prima.
Prima.
Prima.
*y-
nj.
IN D y A B y S LINEIS.
Linea fecunda. Redtangulum e
lineis.
IN T B^I B V S P B^O P O B^T I O N A L I B y S.
Tertia,
Quadratum c
prima.
Quinta pars totius continua-
tas minore Tegmento.
Minus Tegmentum.
Quadratum e fe-
cunda.
Quadratum e fe-
cunda.
v. in qjs at y o ^ c o n r I N y e p ^ o p o b^t i o n a l i b y s.
Quarta.
Cubus e prima.
Cubus e fecun-
da.
V].
Qu_adratum Tegmenti primi ,
Quadratum Tegmenti fecundi.
Bis re&angulum Tub Tegmentis,
Aggregata,
SECTIO QJg ^ € D B^A T L
Duplum quadratum primi Tegmenti, A
Duplum quadrati fecundi, /
vel, aggregata, > aquantur Quadrato Totius
Miniis differentia quadrata Tegmen- \
torum,
T
vtf. SECTIO c y B I,
Cubus Tegmenti primi.
Cubus fecundi, J
Triplam Tegmenti primi in quadratu TccundiA- aquantur Cubo Totius.
T riplum fecundi in quadratum primi, \
. . .... Aggregata, J
A, 'd qua pleni funt Aped&ixeon Geometria libri.
6. QV AT^VO K continue Proportionalium Diagrammata.
In Primo.
Triangula A C B & A F D Jimt aquiangula.Et Ji a pun&o D ducatur linea per E ccntrnm,cad.et in pmBo G,vnde angulus A B G recius , eduBaJubten sd
B G, & ita B C fecunda, ejl proportionalis inter A C primam, <y C G feu D F tertiam.
In Secundo.
Vt B E ad E D,ita B C feu E F ad A C.Eii autem E D proportionalis inter B E (y E F.
In Terrio.
BE^EDf/t/iBC ad A C,feu E a. Erit autem E D proportionalis inter B E & B C,fe E D fe habet ai E A, vt quadratum E D ad quadratum B Cjcu
vtquadratnm B£ adquadratum c Et. Sane vt o [a ad [.iic,ita [ax, ad /a coi deo que B ja ad /x cojta quadratum B /a ad quadratum /au sunt autem aquiangula
T 'riangula B [Ait C^BE D: ideoque vt B /a ad jAvyta B g ad E D,y confequenter eorum quadrata funt homologa. At vt B /a ad /aco, feu B G, cjfe E D ad E A
o frenditur. Quoniam B [ail& B G £ funt aquiangula.ita B /x adii G,c£tvt , x -a ad G 'f ^ jc ante ad E D,ett vtB ^adB E ; item Gpadi\JfivtG cofen B u
ad E ce feu B E, funt enim aqmangda <a E A C2 r ’ Ergo (x x ad E D ejt vt GtadEx,y permutando E D ad E A vt /a jt ad G £, CA confequenter vt B
ad [aco.
D iij
30 FRANCISCI VIET MI, VNIVBRSALIVM INSPECTIQNVM
7 EX dato RECT ANGVLO aquali ei,quod fuh Lateribus continetur jum
Differentia^ e l aggregato eorumdem 3 dantur Latera.
CONSTITVTIONE DV O RV M P L A N O R V M RECTANGVLORVM
T RI A N GV LO RV M In iam propofito Digrammate.
L
AD
Differentia dimidia
terminorum extre-
morum,,
feUjMaior.
CD
Differentia dimidia
terminorum me-
diorum,
feUj Minor.
II.
AB
Differentia dimidia
Maior, plus extre-
mo minimo ter-
mino, feu,
Dimidium extremo-
rum terminorum
aggregatorum.
CB
Differentia dimidia
Minor, plus medio
minimo termino,
feu,
Dimidium medio-
rum terminorum
aggregatorum.
IN ARITHMETICIS PARADIGMA.
Eflonumerus Z40 fadlus ex duobus numeris, quorum differentia datur 14. Placet exquirere qui jintiUi numeri. Si adfumatur numerus
quaternarius ad terminuvnu , u diuijor numeri Z40 dabit 60, qui erit alius terminus , ambo medij vel extremi. Horti differetia 56. At proponitur
differentia minor terminorum ignotorum, nempe 14 .qui ideo erunt medij ad adfumptos. Quadratum 7 dimidies differentia mediorum efl 4.9, quod
demptum a 784 quadrato z8 dimidia differentia extremorum terminorum relinquit numerum 73 3 fubducendum 'a 10x4, quadrato 31, nume-
ri conflati ex dimidia differentia extremorum plus minimo eorumdem , & remanebit z8 p quadra-
tum 17, numeri videlicet minimi medij plus differentia dimidia qua medius maior eum excedit. Efl
igitur numerus ille minimus medius 10 ,alter z^&vt 4. ad 10. ita X4, ad 60. At dum datur >n d
differentia, fed aggregatum, tunc a pofleriore triangulo inchoanda operatio efl, non difimili deinde m e~
thodo exequenda.Vel,& facilius ex fubiedlo alio Diagrammate, A quadrato «, $,qua efl femifis
& r. co aggregatarum, auferatur quadratum <a, quod dabitur, cum pofsit redi angulum ex in^ay
cui datum efl aquale . Refiduum erit quadratum fl, Differentia inter dimidiam aggregatarum, &
fegmentorum e*, vel tua Et huc pertinet v.Propofit. lib.ij.Elemcnt.Euclid. Tradit item Diophan-
tm lib.j. rerum Arithmet.propofxxx.
«Ss
AD CANONEM MATHEM ATICVM, LIBER SINGVLARIS.
E X dato R E C EA NGVLO aquali ei.quod fub Lateribus continetur s cum
Ratione eommdem 3 alterius ad alterum 3 dantur Latera,
'ANALOGIA V NA i E CATHOLICO THEOREMATE . SVBTENSA s IN
< *
CIRCVLIS , SINVS'VE > ESSE VT DI AMET ROS.
Redtangulum cx Ter-
minis analogis 3 feu da-
tae rationis.
ii.
m.
Quadratum alterius e
Terminis analogis.
Redtangulum ex Ter-
minis veris.
IUI.
Quadratum alterius j
e Terminis veris.
Potentia i g>.
IN APODICTICO DIAGRAMMATE,
Potentia «0. Potentia t sr*
Potentia Aar.
Vnde latus ipfum,per quod tan-
dem diuifo Re&angulo, prodi-
bit latus reliquum.
x
Ary,& tffi, Latera qut-
comprehtnfum Reclangit*
Jeu v t,^pfe habent, vt & 0
fita. Sub quibus videlicet
Ium tequale ejl quadrato rrf,
ad @ y } exhypotheji.
40
FRANCISCI VIETyEI, VNIVERSALIVM INSPECTIONVM
XVI.
PLANI OBLI QVANGVLI IN OBLIQVANGVLA
fitti Theoria^ adfequendi Methodus aliquibus datis.
Triangvlvm Obliquangulum
Si fecetar in duo obliquangula
Et detur Angulus Tedus
& ratio Tecantis
ad alterutrum Tegmentorum
Ipfa etiam ratio Tegmentorum,
Triangvla erunt data,
ABD,
AGD, &c GBD,
B,
DG,
GB,yel GA,
GB ad GA,
QVATVOK QVAE SEQVVNTVK JN ALOGIIS,
Defcripto Circulo circa Triangulum, & duclh a centro tribus Semidiametris, vnd per jwnBum i [eBionis t
altera orthogonia ad Bafirn, tertia orthogonia ad Lineam fecantem.
i.
AB
I. B afis Teda, T ota, in
partibus lineae Te-
cantis.
ii.
DG
Linea Tecans in par-
tibus datis.
ni.
AB
Bafis Teda in partibus Se-
midiametriTriangulum
circumfcribentis,
SubtenTa duplo totius an
guli Tedi.
IUI.
DG
Linea Tccans in partibus
quoque eiuTdem Semi-
diametri,
SubtenTa congrua»
DG BG
II. Subtenfa congruat Segmentum BaTeos
ynum, in partibus, e~
luTde Semidiametri.
GA
Segmentum BaTeos al-
terum, in iifdem.
AL
Produdio conguae Sub-
teTae. VndePeripheriaa
Linea Tecate ad Periphe-
rie produda, SubtenTa.
AD CANONEM MATHEM ATICVM, LIBER SINGVLARIS.
53
/.
RO
III. Subtenfe pfodudae
dimidiae Bafis.
//.
GR
Differetia inter Sub-
tcnfam dimidiam
produdam , &c con-
gruam integram.
II L
G
Sinus Hypothe-
ticus acuti, vt Re-
dii,
OM
IIII. Bafis Anguli totius
fedli.
MG
Differentia inter Ba-
fim fedam , & bifc-
dtam.
G
Sinus Hypotheti-
cus acuti, vt Redi.
mi .
g°a
Faecundus differentiae
inter dimidiam peri-
pheriam quam fubten-
dit Linea fecans pro-
duda , & peripheriam
accuratam , qua differt
angulus fedus a bife-
dlo,fi bahs eft bifeda,
aiioquin aequabilem.
Vnde ipfa peripheria
accurata, vel aequabilis.
g° n „ , -
Faecundus Proftaphe -
refeos peripheriae eius
squabilis , qua differt
angulus {"edus a bife-
do.Vnde ipfa differen-
tia accurata.
UACTBNVS VE PLANIS.
E
5 +
FRANCISCI VIETAS I, VNIVERSALIVM INSPECTIONVM
nAN 0'N M AT H E M Ai: IC V S «min PLANIS tantum, verum-
etiam in S P U aP> RICIS fatim exercet officium , immo vero nobilius , ei admiratione dignius ,
qui P T R pt Lid IDV JM adfe5lionibus& quemadmodum ji f\[ G V L I SOLIDI
circa GLORI centrum fiant fedulb non attenderit.
XVII.
TRIANGVLVM S PH JE.RICVM RECTANGVLVM
' !
non difsimilibm d Plano notis perpetuo dejignandum , aut dejlgnari fub4ntelligendum,
mi cuique vero termino , alio quam Refto angulo ,fuum inejfe Triangulum 5 Juas ad
Sinum Refti, pro trina ferie , exercens oAnalogias.
t
AD CANONEM MATHEM ATICVM, LIBER SINGVLARIS.
XVIII.
TR IeA N GVLI S P U VE RI C I RE CTA NG VLI
DECEM MET MMORVHOSES.
— — - — *
T «
C
AB
A
C B
B
AC
II
C
AB
B
A C
A
C B
III
C
Ae
A
x
zz
AX
IIII
C
SZX
B
A
AfZ
AX
V
C
A£r
£X
AX
A
X
T vi
C
A
AB
CB
A&
X
VII
C
B
A B
AC
ex
A
VIII
c
A
Ae
X
AB
C B
IX
c
B
£X
A
AB
A C
X
c
&X
AfZ
AX
B
A
■m
INTERSECTIO , Nota eji ■&a.gi£7r\ypdofi&'TZ)5 , Bajcosjeu Refidttx.
3«
FRANCISCI VIET y£ I, VNIVERSALIVM INSPECTIONVM
XIX.
CANONICjE DECEM IN SFHjERICO
TRIANGFLO
RECTANGVLO
, I-XMDIV EXPETITAE, NECDVM aINTEHaSC
e x H ibit qAN ALOGI Sexies etijlm pro
NVMERO T ER M IN O RV M REPET IT>AE,
QVjA RVMduftu, fi ex terminis sphaerici trimngvli rect^ngvli duo quilibet,
prater ^ ngvlvm rectvm , dentur, vitro qu&fitus terminus, vel ex vnd operatione Logi-
filices fius Multiplicationis, fiue Diuifionis,vtr a commodior videbitur, via, mnoteficit . *
DEC^iVlS I AE
DECADIS IIAE
PENTAS.
PRIMA
PENTAS
SECVNDA
PENTAS
PRIMA.
Torus Sinus
Sinus Sinus
Totus Facundus
Facundus Sinus
Totus Sinus Facundus Facundus
i
C AB
A C B
VI
C AC
X
C B
i
C A c
A CB
ii
C AB
B AC
VII
C C B
A
A C
ii
f
m
c C B
B AC
\ 1
m
C AZ
A X
VIII
C AZ
CB
X
C AX
A Z
mi
c zz
B A
IX
C AZ
A C
A
iiii
C AZ
B A
V
C AZ
ZX A A
1 x
C X
A
AX
, v
C Z
ZZ AZ
SVB DECADIS I ae
SVB DECADIS II AE
PENTAS
PRIMA
PENTAS
SECVNDA
PENTAS
PRIMA.
Totus Hypot/ 4 -
Typot/ 4 Hypot/*
Torus Facundus
Facund* Hypot/ 4
Totus Hypot/ 4
Facund* Facund*
i
C AX
A ZX
Yl
C AZ
B
ZX
i
C AZ
A ZX
II
m
C AX
% az
VII
C ZX
A
AZ
n
T
I II
C ZX
Z AZ
C AC
A B
VIII
C AB
zz
B
C AB
A B
ini
C C B
Z A
IX
C AB
AZ
A
1 1 II
C AB
Z A
V
C AC
C B AB
X
C B
A
AB
V
C B
C B AB
AD CANONEM M ATHEM ATI C VM, LIBER SINGVLARIS.
57
£ko t> compendium longe tabulas omnes ABronomicas, tabularumque farragines fuperat,
edfque demum valere iubet , mediocriter Arithmetica gnaris ad abditiora ABronomices
viam patefaciens ad reparandam infaurandam pene collapfam nobilem fcientiam,
atque adeo ipfarum Hjpotheflum nexu, quo adfiringunt, liberandam, miram jpem, & ala-
critatem animis inducens . ^
DECADIS
JI AE
i
VEC^DIS II I A *
PENTAS
S ECVNDA
PENTAS
PRIMA
PENTAS
SECVND A
Totus Sinus
Ftecund 9
Fajcund 9
Totus
Sinus
Hypot/* Hypot /“
Totus Sinus
Hypot^Hypot./*
VI
C
B
A B
C B
i
C
B
A
C B
VI
C
AZ
AB CB
VII
c
A
A B
A C
ii
i
m
c
A
B
AC
VII
c
ZS
AB AC
VIII
c
C B
AJZ
B
c
ZB
A
B
VIII
c
A B
AZ S
IX
c
A C
ZB
A
mi
c
AZ
B
A
IX
c
A B
ZB A
X
c
A
AZ
AB
V
c
A
ZB
AB
X
c
B
AZ AB
SVB DECADIS II Ae SVBVEC^DIS III A *
PENTAS
SECVNDA
PENTAS
PRIMA
pe"ntas
SECVNDA
Totus Hypot.i*
Fscund 9
Ftecund 9
Totus Hypot./*
Sinus
Sinus
Totus
Hypot.A Sinus
Sinus
VI
C
B
AB'
ZB
I
C
B '
A
ZB
VI
C
A C
AS
ZB
VII
c
A
AB
AZ
II
III
c
A
B'
AZ
VII
C
C B
AS
AZ
VIII
c
j 2tZ
AC
B
c
C B
A
B
VIII
c
AB
AC
B
IX
c
AZ
CB
A
IUI
c
A C
B’
A
IX
c
AS
C B
A
X
c
A
A C
AB
V
c
A
CB
AB
x
c
B
A C
AB
38 FRANCISCI VIETyEI, VNIVERSALIVM INSPECTIONVM
J N DECADE primi prioris Pentados Apodixis pendet ex iis qux demonjlrantur a Regiomont. lib. 4 . Triingul propof.i6.& 19 .^ 7 *
alioqui fatis patet ex fubiedld Trianguli Sphxrici recl anguli , egnfuorum Verticalium figura. Vndeetiam ejyntheji Jupra conjlitutx
funtdenx Met amorpho fes.
POSTERIORIS Ventados demonjlratio pendet ex ratiocinatione qua fequitur.
I n Prima Pentade
r Sinus
Totum
r
Sinus
Sinum
A
C
JBr
Ac-G'
At
\ Sinus
Totum
Sinus
Exeundum
vt
> A
\ad} C
ita
)
At
\ad} Ac
Sinus
Sinum
Exeundus
Sinum
Er trO
O
v- Ac
c.
Ac
<kJ&
Jt EM, /V; prima Pentade
<- S/#«*
B
Totum
C
t
_ «SVVm
Ac
Sinum
-eAr
At
i Sinus
) B
Totum
{ad} C
ita
n Sinus
) <Br
Exeundum
{ad} sr
Ero-o
O
Sinus
^ &
Sinum
Ac
1
Exeundus
L ■B'
Sinum
-G'#'
E R G Oper Synthefim & c*uMd£
A T, ex eadem Pentade
Conse qxente r Redlangulum C
totius in Ac<B" xquale ejl Redi angulo
At Exeundi in -B" Exeundum , cum
verum que xquetur Redi angulo
fnus in Tdr <ET ftmrn.
'Z/f
r Exeundus
Ac «ft/
Sinum
<k€r
ita
r Sinus
Exeundum
ad dtT
(
) Totus
Sinum
< .S7##j
Sinum
'Ztf
} C
Ac-G"
ita
^ -ea-
ad Ac •B'
-
cum vtru-
que bini ter
mini fe ha-
beat vt Ac
finusad iQr
finum.
C Tof#*
Exeundum
r Exeundus
Sinum
G
ad Ac
ita
\ ad
Ac#
*A N ALO G I A videlicet fecundx Pentados poflremo loco repofta. Cxterx eiufdem
Pentados Analogix conflant ex ferie Mctamorphofebn.
AD CANONEM MATHEM ATICVM, LIBEB SINGVLARIS
35>
MELI QV ^iE Decades & Sub-Decades creantur per Synthefesjvi 'praecipue harum u4mlogian ex Piam repetitarum.
/.
ii.
///.
illi.
I
Totvs
Fecundus
Fecundus
Totvs i
Peripherie
Refidue
2,
To T V s
Bypotenufa
Sinus
Totvs
Peripherie
Refidue
3
Totvs
Hypotenufa
Sinus
Totvs
Refidue
Peripherie
DE N^iRlVS autem ideo fuit neceffarius numems, quoniam tantus ejl Metatbefeon datorum terminorum cum non datis.
Vtecce ,
TERMINI SFH^EEJCI RE C T N GELI
funt
C AB
A C B |
B AC
;rmini dati, vel erunt
Quaerendi ver s 0
Quosfuppeditat Analogia
C AB A
C B
i.
B
x.
vel
A C
IX.
C AB CB
B
VIII.
A C
V.
C AB B
A C
II.
C A CB
B '
IIII.
.
AC
VII.
C A B
AC
IIII.
C CB B
1 .
AC
VI.
vel dyafa&H;.
40
FRANCISCI VIET^CI,
VNIVERSALIVM INSPECTIONVM
XX.
AN ALOGI AE ITEM
SEXDENAE
abs Sinu Tdpfli feti Toto .
r
DECAS
PRIMA
“I
r"~
DECAS *
Sinus
Sinus
Sinus
Sinus
Sinus
Fecund*
Fecunc
9 Sinus
Sinus
Sinus
Fecund 9
1
Fecund 9
I
B
A
AJA
AA
VI
A
A
A C
A B
1
A C
A
A
AA
II
A
A
■A A
A A
VII
B
A
C B
AB
11
CB
A
A
AA
III
JAA
A
AB
A C
VIII
A
C B
AA
AJA
iii
AA
C B
A
AC
II II
AJA
A
AB
CB
IX
B
A C
AA
AA
iiii
AA
A C
A
C B
V
' A
C B
B
AC
X
JAA
A
A
AJA
X
A
A
CB
A C
1
SVB.DECAS
r-
PRIMA
SVB-DECAS
A ^
*
-""N
Hypot/* Hypot. j4i
Hypot/*Hypot/*
HypotA Fecund’
Fecund*
HypoA
HypotAHypotA
Fecund 9
Fecund*
I
A
A
A C
A B
VI
A
A
AIA
A A'
1
AIA
B
A
AB
II
A
B
C B
AB
VII
A
A
JAA
AA
11
JAA
A
B
A B
III
C B
• A
AA
AJA
VIII
A
AA
A B
A C
iii
A B
JAA
A
AJA
I III
A C
B
AA
JAA
IX
A
AJA
A B
C B
iiii
A B
AJA
B
JAA
V
A
jaa
A
AJA
X
C B
A
B
AC
V
B
A
JAA
AJA
Comparantur per Synthcjes,& <equa potentium Rcfflangula Theoriat.
XXL
CVM QV AURATO VEN1QVE SINVS RECTI ANALOGIAE DVAE.
1.
II.
III.
1111-
Quadratura Sinus Redti
Re&angulum
Sinus
DifFcrentia inter linum verfum CB,&
Sinus
Sinum
verius
verfum Peripherie , qua diferepant
C
AB AC
A
AB & A C.
Differentia inter Unum verfum A C, &
verfum Peripherie , qua diferepant
C
A B
C B
B
A B & C B.
Vide Regiomont.propofit.z.lib.j. T R1 AN GV L>
SECVNDA
AD CANONEM MATHEMATICVM, LIBER SINGVLARIS.
SECVNDA
r —
Sinus
Sinus
Faecund 9 Faecund*
VI
e
A C
A
A B
VII
Ac
C B
B
A B
VIII
C B
Ar-R
A
Are
IX
A C
At
B
et
X
Ac
e
et
Are
i
n
m
ii ii
DECADIS
TERTIA
PENTAS
A C
e
Ac
Are
CB
Ac
e
Are
Are
CB
Ac
A C
Are
AC
e
CB
e
A:
CB
A C
VI
VII
VIII
IX
1 PENTAS MIXTA
Sinus Sinus iHypottHypot/*
AjB
B
e
Ace
A;B
A
Ac
Ace
Are
A
Ac
A C
ee
B
e
C B
Ace
ee
C B
A C
*
SECVNDA
r vA-^ -
Hypot/* Hypot/*
— 1
Farcund 9
Faecund*
VI
B
Are
Ac
ee
VII
A
ee
e
Ace
VIII
ee
A B
Ac
A C
IX
Are
AB
e
C B
X
A
B
C B
A C
I
II
III
IIII
SVB- DECADIS
TERTIA
r
Sinus
HYP
Sinus
0 pentas
Hypot-/ 4 Hypot./ 4
hypopent
Faecund 9 Faecund 9
AS MIXTA
Faecund* Faecund’
te
B
A
AB
VI
Are
e
B
AC
ee
A
B
A B
4
VII
ee
Ac
A
CB
AB
ee
A
Are
VIII
A B
C B
ee
Are
AB
Are
B
ee
IX
AB
AC
Are
Are
B
Ac
ee
Ace
X
B
Ac
A
e
41
XXII.
ET CVM SINV TOT O i ET EIVSDEM QVMDRsiTO, D V JtE ITEM MN uiLOGI^E.
I.
,$ RedtiJ Redtangulum
Sinum
Quadratum Sinus Redti
c
C
11.
Redtangulum
Sinus.
et
Ace
{*“!
B
A
in.
Totus.
////.
Sinus.
C
c
Ac
e
Ex tertia- Analogia prima Decadis Reftangulum in finibus Ace in A ejl aquale ReElangulo C in -R. addantur ei ReSlangulo quinque
numerales circuli, illud eji ducere reclagulum in ftnum totum. illud idem ducere Jinum e in quadratum Sinus Totius, quod fuum latns
totidem circulis excedit. Notantur a Regiomont .Propof] t ^..lib. 5. Triang. Sedotiofe funt& qu<& alio quin ad numerum Canonicorum
potuerant afeendere.
I
41
FRANCISCI VIETyEI, VNIVERSALIVM INSPECTION VM
XXII.
TRIANGFLVM SRHjERICFM 0 BLI QFA N G VLVM.
A
IN O B L I QVM N G V L I S Sph&ricit dandi futtt tres t er mini. & jecatur itent Oolicjuangitlum in duo Recian^ula^educio commode
Orthogonio per angulum non datumgat o tamen Uteri adiacentem.
I. TERMINI T R I At N G V L I S P H ME R I C I O B L I Q^V M N GV LI
S eris Analoga, ex Catholico T he ore mate, Sic latera ad latera /vt
Sinus ad Sinus angui orum, qui a lateribus fubtenduntur.
Angulus
verticis.
BD
Balis.
D
AB
Angulus ad ba- Crus
fun dexter. finiftrum.
B
w .
fi m finifler.
Angulus ad ba- Crus
AD
'rus
dextrum.
AD CANONEM M ATHEM ATICVM, LIBER SINGVL^RIS. 43
2. Jidetathefes trium datorum terminorum .
f >■
A
BD
D
b
II
A
BD
AB
III
A
BD
B
•
IUI
A
BD
AD
^ v
A
D
AB
'f XI
«/
BD
D
AB
VI
A
D
B
XIl
BD
D
B
VII
A
D
AD
Xtl
BD
D
AD
C vm
J
A
AB
B
f XIIII
BD
AB
B
^ XVII
IX
A
AB
AD
XV
BD
AB
AD
XVIII
XIX
Ex angulo A
Datis, cum a-
liquo tertio
termino.
Ex angulo B
B AB 8 14 17 zo
D B D 1 11 iz 13
vt in Metath.
vt in Metath.
D A D 7 13 18 15»
A A B 2385)
fiue cadat extra, fiuc intra Triangulum.
alo D
B BD 3 ix H
vti-n Metath.
A A D 47^
Secundum qua: ad Methathefes 7, 8,12, & 9,13,14, bina valet Edudtio.
P O R R O cum dantur latera tantum, vel anguli, opus eft Parafceue, videlicet in Metathefibus 6 & 13.
E ductio Orthogonij.
3 <?
FRANCISCI VIETAEI, VNIVERSALIVM INSPECTIONVM
AD SECTIONES 0 B L I Q^V A N GVLORVM
IN RECT^ANGVL % A > V^AR^ASCEV ,AE.
I .
Ex coaceruatione duarum Peripheriarum, & ratione jlnuum
earumdem 3 difcermmtw P er ip heri a f
r.
Partes analogx
Peripheriarum
aggregatae.
5 " w
t QF*
AC
Sinus Refiduidi-
midij Periphe-
riarum aggrega-
tarum.
o
e Analogia vna e Geometrica fecEone.
ii.
Partes analogae Maio-
ris Minorifve Periphe-
rie.
ni.
mi.
gy, vel <p jul
De in ex Plano re tt angulo altera
CB B
Subtenfa Peri- Subtenfa Peripheriaram ag-
pheriarumag- gregatarum dimidia , plus
minurve C B, finu equabiii
Proftapherefeos.
B gj vel, $ B 5
gregatarum
e<p
Sinus aequabilis Profla-
phaerefeos.
Acutus, 'vt
Redus.
A
E F JECrUD O.
Proftapheraefis vera, Abla-
tiua dimidio aggregataru,
vt prodeat peripheria Mi-
nor, Additiua,vt Maior.
SIC ET IU ABJTHMETICIS STNT aLOGI TBgJMINI.
n.
Proportio magnitudi-
num aggregata.
Magnitudines aggre-
gat x.
ni. mu
'Terminus pri- Prima Magnitudo.
Imse rationis.
Secundae. Secunda.
Quibus vti fit tutum efi in minimis, vbi linea Ambitio fi & retia fere coalefcunt ,
AD CANONEM MATHEM ATICVM, LIBER SINGVLARIS.
37
2. Ex differentia duarum Peripheriarum $ ratione fintium earumdem 9
dantur Peripheria 3
Analogia item vna e Geometrica fictione.
r*
Partium analo-
gam diferepantia.
€ ft
A C
ir.
Partes analogx periphe-
riae Minoris.
///.
Subtcnfa diffe-
rentia? Periphc-
riarum.
rrn.
fiv gy
Dem ex Plano re E angulo altera .
C B B
^quabilis Minoris peri->
pheriae Sinus,
Sinus differentia JEquabilis Minoris finus,
Peripheriarum plus finu dimidiae diffe-
Reliduae. rentix.
A
E F ^ECVKD 0.
Acutus, vt Redlus. Feripheria vera Minor
plus dimidia differen-
tia, vel Maior, miniis.
I N Piam Triangulo Mera vtifunt operatio 'exigit. fub notu indicamus. Angulos vero e fuU Peripherie fere denominamus quemad
m °aT.ff! atmi V 0 !**» Sphaerico fene vbique memores adfumendos effein operatione numeros fecundum notarum adfriptam adf-
Bionem.
i- i u
Excefsus proportio- Exceffus magnitudinum,
num.
* Ptolemxi exemplo cap,$. lib. 13, pay, ug eos .
in .
r Terminus pri-
^ mx rationis.
C. Secundar,
1111.
Prima Magnitudo.
Secunda.
FRANCISCI VIETASI, VNIVERSALIVM INSPECTIONVM
^Analogia Angulorum in feffiione.
QZ/ 4 m pr&feat perpendere 3 dum ex angulis eruuntur latera.
A
E' S
I N V.
(
J 3 T
a- ^
b A c
dAc
Complementum
anguli ad Balim
finiftri.
Complementum
anguli ad Balim
dextri.
Pars anguli ver-
ticis in finiftram.
Pars anguli ver-
ticis in dextram.
A ejl Apud Regiomont. propof 20. lib. 4. Tmng.
CV M detur coaceruatio pcriphxriamm b A c & dAc, & ratio fimum cavum dem, dantur
fmguU ex Parafceue.
AD CANQNEM MATHEMATICVM, LIBER SINGVLARIS.
47
4., S effio Trianguli datorum laterum ad adfequendos angulos.
D K; S "'VI7 C i r ^V fuper “f ul ° A ' VC P°l°.&^ e um producuntur latera data, vel ipfc eafecando contra-
int, prout Aii, vel A D lunt quadrante maiora, vel minora.Comode vero AB latus:
&ita.
i minus quadrate femper efto.
Duo confli tuuntur Triangula, aD, & * CB, quorum adfequutione totum Triangulum patefit,
‘ “4-WumAD, ^ ««ffus fupra quadrantem, & B C comple.
Item, ex D * & B C per parafccuem datur D A, propter B D notum.Vt enim in finibm „ -„t c ; f , n .A n
quoque B C ad B «, &1 de6,vt Da ad B C, J D l ad B a. Qu^~S£M cum la^B D (dC,
Secundum aBC&“™m Pf * Fenph r 1 *' A r qUe ,t ^ cxla 1 tcre comparabitur «Sagulum primum,
rentiainter * af^C* qux eft anguf^Aamplitudo^ 1 ^ 311 ^ 11 ^' ^ an ^ u ^ ^ ^ ^ cum P ef ip^ cr ^ C a, diffc-
FRANC1SCI VI ET MI, VNIVERSALIVM INSPECTIONVM
/ Aliter 3 P arafceue dum ex lateribus anguli .
SpHiERicvM Ifofcel.es fit Planum.
Plani,
"Crura aequalia
j AB, Sinus AB Sphae-
nci.
A D, Sinus AD Sphae-
t rici.
Bafis
B D, Subtenfa BD
Sphaerici.
Angulus BAD Plani aqualis BAD Sphaerico.
t t
Sc alen v m quoque Sphericum fit Planum.
Plani.
r Crura in aequalia
i
Bafis
f AB, Sinus AB Sphae-
rici.
AD, Sinus AD Sphae*
l rici.
B D, Potens B D Sphae-
rici Subtenfam , mi-
nus differentia finus
& JCPt Sphaeri-
corum.
Angulus BAD plani, vtimfofc«lc> aequalis BAD Sphaerico.
*pud Rcjriomottt.Propof 34. lib . 4. T vi Angulorum,
Cqmparatvr autem ifta Potens ex Analogiis, fi placet,
Canonicis, conflituto Piano,vt videre eff,Triangulo
redangulo.
‘Potens
AD CANONEM MATHEMATICVM, LIBER SINGVLARIS.
6. R urfus , Vt e Lateribus emantur oAnguli , aAnalogia in
Obliquangulo cum Quadrato Sinus recti.
Re&angulum fub Bnu-
bus Crurum.
c
Quadratum
Sinus redti.
Differetis inter linum verfum
Bafeos , & fmum verfum tantae
Peripherice, quanta diferepant
Crura.
Sinus verius Ansu-
C?
lia Cruribus com-
prehenfi, fcu quem
Bafis fubtendit.
Sinus A Bj in Sinum A D.
C,/Vz C.
Differentia inter Verfum B D &
Verfum differentia AB (ff AD.
Vcrffs A.
Sinus A Bj in Sinum B D.
C, in C.
Differentia inter Verfum AD &
Verfum differentia AB & B D.
Verfus B.
Sinus ADj in Sinum B D-
C, in C.
Differentia inter Verfum A B &
Verfum differentia A D er B D.
Verfus D.
P ropef.z. Ub_v.Tr i ungui. Regiom.
/. AN ALO G I A denique figmentorum Bafeos Crurum fn Anguli
Verticis bifetfione.
A.
Crus finiftrum.
AB
Crus dextrum.
AD
Segmentum Bafeos Cru-
ri finiftro conterminum.
BE
Propof. j. Ub. v.Triang.JRegiomottt.
HuSCTENVS DE SP H^iERlClS.
Segmetum Bafeos Cru-
ri dextro conterminum.
ED
G
50 FRANC1SCI VIET-&I, VNIVERSALIVM INSPECTIONVM
VJE non funt p lana , vel s P H PE R I G Pi fib eitifdem Diametri Circulis defcripta E R I p[ 2\f-
(j P LPiy fd vel eMx.oe^u , vel ex Peripherie maximorum & non maximorum Circulorum compada , vel aliter ex redis
meis & curuis mixta, prcef cripta carent methodo, fecundum quam de Lateribus & Angulis J\z[ P E H E JVL P E I-
cps ratio cinetur accurate. Eorum tamen in P L A N I S P A Ai PICIS qiindmttnm mtitix efi, CANONE
MATHEMATICO nullis non in amfr adibas confficuum lumen prxbente , & in trita ab artificibus via , innumeros
fiupulos, & fakbmjn quos impingunt jndicante.
XXI III
TRIaAN GVL VM P LoAN I S P H PERIGVM.
A
A } & B, Anguli Semi-Circuli ex Diametro 8c Pcripheria.
i. IN PlamfthAricis K&Qo^otaTepci.
i. Vt Diameter ad Diametrum, ita cft Pcripheria ad Peripheriaan Papp. Thcor.^likxj.
Angulus ex Peripheria & Diametro minor efl: angulo Redo,fed maior quouis Acuto. Euclides
Prop.i6.lib ,iij. E lentent.
II.
AD CAMONEM MATHEMAT1CVM, LIBER SINGVLARIS.
V T Periphsria remeetur ad partes Diametri ^ e contra Adpofiti Numeri .
Periphcria in partiurmqualium
Circulus totus aeftimatur 360.,
fexagefimis.
io, 8oo,j^i-- 0 - a -
IOO, ooo, °°°> 0 0
Hh 77
Periphcria in partibus Diametri, qua-
lium Diameter 200, OOP 000.00'
314
2 , 908, 88 2 , °ss, 7 t
IO, OOO, OOO, 000,00
E X limitibus Mlmloplz Perimetri Circuli ad Diametrum ante adm tatis.
..O
3 . J^T fecentur Magnitudines media & extrema ratione , vel fe&a compleantur,
vel -etiam continuata d continuatione fegr egentur , Adpo/iti Numeri.
■ Tota.
1 00, ooo 3 m
261 , 803, ?98, 89
1 6 1, 80 3, s 98 . s 9
Maius Tegmentum .
61,803, * 98> 89
161,803, 598,89
I 00, ooo, 00 °- 08
Minus Tegmentum.
38,1^6,:
fio I. 1 z
I OO, OOO, °°°’ 00
61 , 803 , S 9
Tota.
I 00, ooo, °°°.°°
I 2 7, 20 I, £l±_2C
Proportionalis inter totam & maius Tegmentum.
78. 6I5. U 7.77
100 , 000 , ooo ' o °
Tota continuata minore Tegmento.
138 , 196 , 6oI ’ Ii -
I 00, OOO, ° 00 ’°°
3 61, 80 3, i 9 . s ±?x
Minus iegmentum.
38, 1 96, go1 - 11
27, 6 39jii-°— —
I OO, OOO, °°. °i2_°
A- G EO D JE SI A triangulorum.
simplex.
Planus ex Bafi tota,& Altitudine dimidia, vel Altitudine tota &: Bafi dimidia, efl: area Trianguli.
C Q MP M RMT M. ac primum ,
SifintTriangula aque dta/vel fub aquali B afigunt Analogi termini .
Altitudo primi Altitudo Tecundi. Triangulum primum Triangulum Tecundum
Trianguli.
6 a fis primi.
Bafis Tecundi.
Tub aequali Bafi. fub aequali Bafi.
Triangulum primum Triangulum Tecundum
seque altum. aeque altum.
5 2-
FRANCISCI VIETjEI, VNIVERSALIVM INSPECTIONVM
Si Angulum Angulo habent aqualem.
Rcdangulum fub late- Rcdangulum fub lateribus
ribus primi Triangu- fecundi.
Ii aequalem angulum
comprehendentibus.
Triangulum primum Triangulum fe-
aequalis anguli. eundum aequa-
lis anguli.
Ad qiiaim Triangula.
Bafis primi. Latus fub quo & Bafe fc-
Triangulum primum. Triangulum fe-
eundi continetur squale
eundum.
Redangulum ei quodfub
Altitudinibus.
Altitudo primi. Latus fub quo & Altitudi-
Triangulum primum. Triangulum fe-
ne fccudi cotinetur aequa-
eundum.
le Redagulum ei quod fub
Bafibus.
s-
G EO D AE SIA Circuli.
i.
ii.
Circuli funt vt a Diametris Quadrata.
Triangulum redangulum cuius Bafis eft vtSemidiameter Circuli,, Altitudo vt Perimeter,
Circulo cft aquale. Et fi Altitudo eft vt Peripherie Tegmentum aquale ares Sedoris.
^4 rcbim.lib.de dimenfione Circul.
6 m G EO D AES I A Sphararum,
Sph xv x funt vt a Diametris Cubi.
7. qA D Circulos 3 Superficie fque Sp hararum e Diametris , harum feliditates
e Cubis 3 ^ e contrd 3 Adpofiti numeri.
Circulus. PUm fHferfieiis.Sny^undruflii Spherici fxpcrjicttj.
\ 314,159^65,36
78,539,816,34
I OO, OOO, OOO, OO
Soliditas Sphaerae,
4, 1 1 8, 9 1 3, 5 3 8
5,13 6454, 411
Diameter.
Z O O, OOO
1 0 0 , 000
1 5 9, 517
Z, OOO
*■» 1 5 5
Quadratum Diametri.
4 °o, 000, 000, 00
I 00, OOO, OOO, OO
154,647,908,94
Cubus
8 , OOO, OOO, OOO
I O, OOO, OOO, OOO
S. AD Spharas e Diametris e contrd,Archimedaa me n fur a.
Diameter. Quadratum Diametri.
I
i, 5 oo
Cubus.
— dinti
,00 o
654.0 o
Sphaera.
P apauer. /<«. Pars » Arena. f" e -
X 10,000
terreni Globi Geographica methodo taxauit ex obfimatis rchimed.es certorum fladionm ad ratione ex ambitu Arguit Dia-
metrum:ad quam demum reducit ipfam Sphaera Jlellamm inerr Antium gr Mundi Diametrum ad fummum, atque adeo ex eius Cubo arenae ipfis, quotquot
a tanta Sph ara pojfmt comprabendi, propter notam Stadiorum tn Digitis dimenjionem, exhibet analogice numerandas . Lib.de numero <y£remt.
a
AD CANON EM MATHEMATICVM, LIBER SINGVLARIS.
53
OVADRATVRA
Hippocratica ME NI SCI,
7 \ B
rriangulum Planum redtangulum A B C-dEqualePlanilphxricoGBE.
ESI enim A B E ociam pars Circuli } cuius Senii diameter A E- Item G C B efl quarta pars Circuli, cuius Semidiameter A C. ^At A B
feu A D potefl duplum AC. Itaque tanta .efl vchua pars Circuli fub Semidiametro A E, quanta quarta fub Semidiametro A C.
^Aequalibus igitur auferatur eaaem pars E C B, Refidua G E B & CAB erunt aqualia.
Sic totus G D E B Memfcusft aqualis Triangulo eeqiticrnro D A B, <&put ft habet £ C diefis Semidiametri adGE apotomcm eiuf-
demfita E B Peripheria ad G B Peripheriam.
I0 , Ad ARABO LE.
Portio linea cuma A B C & refta
A C contenta, Parabole.
B D, linea iuxta quam pofTunc
ordinatim applicatx.
A D redtum figurx latus ad E F poteftatej vt B D ad B F longitudine, ex Paraboles conftrudhone.
IZi QVADRATVRA
P ARABO LES Euclidaa.
B Vertex Paraboles.
B D Maxima Perpendicularis.
A C Baiis.
Vt 5 ad 4,ita Triangulum i£quicrurum A B C ad Parabolem. ex demonflratisab Euddib.de Quadrat. Parab.
12. L Atm Quadrati Circulo
ClRCVMSCRIPTI,
Inscripti,
200, OOO, ° oo - 0 °
14 L, 4 1 L,
AE c£V aus, 177, 145, iLeaa
Lacus Quadrati inferipti conflat cxceflu,quo a Diametro fupcratur,&: infuper Potente duplum cxceflum.
G iij
;4
FRANCISCI VIETiEl, VNIVERSALIVM INSPECTIONVM
Dua M edia continue proportionales inter Semi-diametrum, ?£ Latm
Quadrati infer ipti.
100,000,^” 1 1 z } 2 4 6, 10 ?
125, 992,11! 141,421,11!
14.. Dua Ad e dia in eadem proportione continua inter L. Quadrati inferipti,
L. c i remnferip ti,feu Diametrum.
141,421,111 158,740,1
oG
178,1 79,1++ 200,000, ii
*/•
i*.
Dm ex his Ale dia inter Semi-diametrum, ^ Diametrum.
^ Norma Duplicationis cubi'.
Ioo,ooo,°l“ 1253992,111
740»-
o G
200, OOO,.
16 . Proportionalis Ad e dia inter L. Quadrati infer ipti, L.circumfcripti.
141,421,115 168,179,11+
168,179,1!+ 200,000,
1 j. Diagramma pro -
0 c
Series earumdem
adnotata
pofi 'tarum Proportionalium.
ctjc , Vt et(p
a e, Vt a A,.
«,£ dimidium
Diagrammate
demonfirata.
1 .
ce j2>
<p @
Scmidiameter.
11.
iii.
ct £
GL A
llll.
ct(p
CO X
i X
Latus Quadrati inferipti.
F.
ct •y
FI.
0L&,
Fit.
cb 1
Latus Qua drati circu-
fcripti. Diameter.
% AV
Proportionalis inter Latus
inferipti, & circumfcripti.
QVAK quidem it* demonjlramur. Vt »0 addita . y ai tflamtm^, cm x qudk proportionalis mttr « y *. w
«,7, ttr.dt^efl proportionalis inter ^ ideo proportionalk
quoq ’*e inter a. 6 ^ ct. '/■ Vt eat fm a. A a a. ip facessita a. y ad o.fe-r ideo osp continue proportionalis poft&y- AS 1 vero
d * habtt « a ? * 0, fo. ^quandoquidem * g eflfiUuplum a.P,& ^fubduplum * * /m /&*,
«M efi eontsmepropomonahum.Lmta vero * , proportionalis eftmtcra. * &t Lw,qua fint Latus Qjudmi inferipti & circumfiripti .
%
AD CANONEM MATHEMATICVM, LIBER SINGVLARIS.
j f. DETECTA tandem reductionis Peripherie ad lineam rectam,^
T ET K. AGON I S MI CI RCPLI Orontiana & aliorum
PS EVDOGRAPHIA.
S i c V t i Angulus Semi-Circuli maior efl quouis acuto, minor autem reBo, ita cuiufiibetPolygoni Circulo infcripti Perimerer ,vel
Amplitudo, minor eft Perimetro, vel amplitudine Circuli: Similis vero Polygoni circumfcripti, maior. Et, vt inter maxi-
mum acutorum , gy reBum non datur homogencus medius angulus , fic neque inter Polygonum infinitorum laterum Circulo
inferiptum, & fimile circumfcriptum datur horaogenea media figura. Superat enim quodam minimo angulum maximum acu-
torum reBus angulus .quod, quidem minimum diuifionem non recipit ab angulo homogeneo , alloqui non effet minimum. „ 4 cquefi -
feratur quodam minimo Polygonum infinitorum laterum Circulo inferiptum it fimili Polygono circumfcripto . quod item minimum di-
uifionem non recipit ab vlld homogened f gura. Sed <vt anguina femi-Circuli medium quoddam efl inter maximum acutorum,gy retium,
Ita circulus medium quoddam ejl inter Polygonum inf nitorum laterum circumfcriptum ,gy fimile inferiptum. Heterogcnea videlicet in -
terhomogenea folum. i it locus non fit in rerum natura Polygono cuipiam ad Diametrum acia, vel potentia fymmetro ,quod amplitudi-
ne , vel ambitu circulo aequetur. Quod vt euidensfat , concipiantur fime duo fmilia Polygona , quorum altenmCirculo circumfcri-
batur, alterum infcribatur,non erunt tam prope inter fe congrua gy a qualia , quin duo dabuntur propius congrua gy aequalia. A dfumptd
enim quamarumlib et partium Diametro futurum tamen efcpt aliquando concurrant alicuius minutulae, Periphcriagy Sinus gy Facun-
dus, v ter que proximus vero inter partes adfumptas, Sinus inquam, id effemilatus Polygoni infcripti , F secundus circumfcripti. foldque
Peripheria inter Sinum eiujdem gy F secundum potejl adftgnari media, folus denique Circulus ( cum fit ratio totius ad totum , quot partis
adpartem ) medius inter duo fmilia Polygona , vnum inferiptum , alterum circumfcriptum , quam maxime inter fe congrua gy aequalia.
Nec moneat quadratura Hippocratica M emfei , fu Lunulae ,ficuti neque quadratura Euclidea Paraboles. Neque enim deferibitur Lu-
nula a duobus Circulis homodiametris,fd i-npoSicifatTpini. At Diametri ad Diametrum analogia rataefl ,vt veripheria ad Periplis-
riarn, gy quadratur ea duntaxat Lunula, quae conflata eflexinterfeBione duorum Circulorum, quorum Diametri funtin ratione dupla,
ita vt S emi di amet er maions fit Utus quadrati intra minorem deferipti. Curua vero linea Paraboles , non tam linea efl , quam meta li-
nearum, no aqualium a Centro, vt Peripheria Circuli fed ina qualium fecundum diftdntiam a punclo f Bionis Uteris rech gy tranfuerf
proportionaliter decurtatarum . Neque ideo quod quadretur Parabole, reBa linea curua Paraboles linea datur aqualis. A 1 fi quadraretur
Circulus, neceffario curua linea daretur aqualis, propter Anhimedaum Theorema de Triangulo ReBilineo circulo aquali fi Bafs Trian-
guli fit vt Radius Circuli , Altitudo vt Peripheria. Quod argumentum etiam ad defruendas Lunulas valet. Solent obijeere ex Mechanicis,
ambitum rota circularis, in plano deferibere lineam retiam , gy filum ambiens circulum fi fecetur,in lineam reBam re cie porrigi, mtt in
circulo non ejl initium, neque exitus, gy fft intelleBu vel mechanica fectione, attamen terminatum minimum femper manet in fuo cur-
uo,quamtumamque continuatum in reBum porrigatur. Quare non ejl ijs interpretibus credendum, qui Tetragonifnum Circuli f ibi-
dem effefed nrfcifi, vel ex Arijto tolu dobtrind contendunt,Nufquam id tradidit Arifloteles diferie,gy f traderet. Euclidi in hac Philofo-
phia parte efl adfntiendam. Erepoyzvdia certe terminati curui 'a terminato reBo validioribus Antiphonis gy Brifonis argumentis fatis-
facit. Archimedes vero , non ideo quod T riangulum reBilineum propof terit Circulo aquale f T rianguli Bafs ft vt radius Circuli Al-
titudo vt Peripheria, conuincendus efl aut quidpiam abf ardum gy otiofum propof lijfe, aut fiiltem , quin ejfet in rerum natura linea reBa
Peripheria aqualis , non dubitaffe , immo vero adferuiffe,gy ipfam etiam , vt commentus efl Eutocius Afcalonita,per fpirales lineas in-
tieniffe. Egregium tanti artificis inuentn nequaquam periijfet eo prafrtim jcculo,quo quas t io de T etragonifmo Circuli tantopere contro-
mrtebatur. Sed non QiJfi put 01/ linea regia Peripheria Circuli aqualis, Geo daf a Circuli prorfas nulla proponeda efl. Ad fmplicifimam
igitur Trianguli Geodafam reduxit eam Archimedes , nulla vel eo nomine non dignus laude. Facillimam pvabuit, gy vfui adeommo-
dam , tamoque iufliorem, quanto propior habetur Peripheria ad Diametrum an alogi a. Accuratam certe non dedit , neque dabit quijpiam
mortalium. Quinimo qui fe rem acu tetigijfe perfuafum habebant gy iamprocinebantf afluo fum evpn^y, tandem comperti fiunt longius
quam pleriquealij recefiffe a vero . Altem latus e medijs proportionalibus inter latus infcripti gy circumfcripti prodidit Orontius aqua-
le quadranti Perimetri , alteru lateri Quadrati Circulo aqualts.At qualium Diameter 200, 000 .talium quadrans Verimetri,\gj,o%o
fere, ex ante conflitutis analogia Perimetri ad Diametrum fecundum viam Archimedaam limitibus. Latus vero medium proportio-
nale, quod indicabat ille, 1 58, 7 40 gy amplius. Item, Latus alterum medium proportionale, maius efl partibus 178 , 179. At Latus qua-
drati Circulo aqualis, minus efl partibus 177, 246. Arguitur no difimili methodo in alijs aliorumque Tetragonflmis error , gy vitium,
vt omnino abhorrenda ft ifla ingeniorum crux,gy opera gy otio deinceps non abutedum, prafrtim vbifemel noBi fuerimus expeditum ,
gy facilem Tetragonifnum, gy fatis propinquum vero.
FRANCISCI V I ET JE I, VN IVERSALIVM INSPECTIONVM
20. VT Peripherie reducatur tyywm ad Lineam Tdedkam^ e contra?
Adpofitum nouum Theorema.
Diameter eft minus Tegmentum Dextantis Perimetri fe&i media 5 t extrema ratione.
t_Au£ld ideo quinta p arte 3 mmus figmentum Afiis.
Et dimidium $ emi diametri auflum quinta par terminus figmentum Quadrantis*
D 4
628, 318.
Seniis Perimetri.
As.
f io. 7 »
Maius Tegmentum Afsis Perimetri.
Minus Tegmentum.
Diameter au£fo quinta parte.
3 88j 3 22 1 p 7. s 1
239, qq 6
2403 OOP
Confindunt in fex primU fere figuris , intra quas fi continet in taxatione Semidiametri Mathematicus Canon,
^£D PJQyfXIM
0 C
SYNTAXIS ^kav^&ofhx/Mp^-
Esto Circulas «, /3 x, F quadrifidus a duabus Diametris bificetur radius aut in a punflo,&per punflum bifigmenti educatur
fubtenfa fecans P eripheriam in y punflofi quo adDiametrum £g J' defendat perpendicularis y\ cequidiflansDiametro ausy. Erit
t\ dimidium radij auflum quinta parte, nempe 60, 000, qualium radius 100,000. Taliumetiam yX 80, 000. Et «,0 1 . izy,ooo,
000,000,^ ouy 1 . 3x0, 000, 000,000. Eflenim X^adfcX vt quadratum at, ad quadratum cte,inJpeflione xv , fibfinemfth -
wmpcav ^inalogiM in Mifcellaneisplanorum.Stdquadratum tLieft quadruplum ad ai. Qualium itaque quadrata ou & ca t a*crre<rata
valent y talium «.e valet 4. Siqualium a,X <& Xf' a?gregata,id efl Diameter 'Perunt zoo, 000. Talium 160,000 finalium
etiam tte Semidiameter 100,000, Vnde 60, 000, dimidium Semidiametri auflum quinta parte eiufdem.Iam in linea Q & poten-
teradij fefqui ait erum ad fumatur ab 00 p anclo linea ce p longitudine ce £, erit Q p , latus Decagoni, maius figmentum Semidiametri fecti
media & extrema ratione. In radio itaque e x, a punflo % adfumatur % v aqualis Qp.&ab v punflo ad A punflum educatur refla y a
Cui parallela definbatur a punflo % ,fecans Semidiametrum / 3 eJ\ ideo producendam in punflo <p. Erit i ap refla, aqualis Peripherice
ex Theoremate Eflenim iX ad eq> vt tv ad tx.jdejl^vt Minus figmmtum ad Totam.
Nec difsimilt via procedendum efl data qua libet alia Peripherie! maiore, minorcue quadrante, vel refla maiore minorent ed, cuius probortio-
naliterfiflx maius fegmetum fit fefqui quintum ad dimidium Semidiametri \ modo quota fitPeripheria illa ad Circuli Perimetrum vel
refla ad Diametrum non ignoretur.
19. CONSECTARIAM
AD CANONEM M ATHEMATICVM, LIBER SINGVLARIS.
>7
2.1. CO WJ ECTA R IV M
A D Quadraturam Circuli abcommodv m.
Latus Quadrati circulo aequalis, fedtum media & extrema ratione, & continuatum minore fegmcnto,po-
tcft latus circo mferipti & inferiori, feu,$extuplum circularis radij.
Et proportionaliter minuendo, Latus Quadrati quadranti circuli .Tqualis,fc<dum media & extrema ratione,
continuatum fimiiiter minore lamento, poteli: radij fdquialterum. Quantum etiam fote]} aggregatum fi-
mis Peripherie x~y.& fimis Ix xl). Refidua.
CO NS ECTARJl PIATIO ET pJQAXIS.
Etsi ex Arcbimedao Theoremate circa G £ o d.s fui m C irci/l i, R ecianmlum fub dimidio S emi- diametri & Perimetro toto co tentum aequare-
tur circulo, dato vero Redi angulo , dare eft Quadratum d aquale. Attamen idem Tetragonifmus non minus commode comparatur 'c
propofito confeSlario.Qucd ita dicitur.
C v Mpt Diameter minus fermentum dextantis Perimetri fidit media & extrema ratione , Maius figmetum, quod ejl proportionale inter mt.
nm & totam, potejl confequenter Redi angulum contentum fub minore & tota , idejlfub Diametro & Perimetri dextante. 1) i mub um
itaque maioris illius fegmenti erit latus Quadrati dextanti circuli aqualis, Potens videlicet Reti angulum fub Scmi. diame; t v ©• (nunc un-
ce Perimetri contentum duntaxat , vel 'fub S emi- diametri dimidio (y Perimetri dextante. Quse potentia ad totius maior,* /c- menti potm ■
tiam ejl fub quadrupla. Erit itaque ,vt dextans ad affem , ita dimidium maioris illius fegmenti ad latus Quadrati circulo a fiuus.Ced Cani-
dium maioris illius fegmenti fidium medta extrema ratione & continuatum minore figmento , efl per interpretationem e v conjiru-
Bione maius figmentum Diametri continuatum dimidio totius, potens ideo quinta pium eiufdem dmidij. Putens igitur jextuplum erit
latus Quadrati circulo aqualis feSlum media & extrema ratione continuatum minore figmento. Et EccXoyuii, Potens jjfiuAUernm
erit latus quadrati quadranti circuli ecqualis felium (c* continuatum vt fupra.
IN Numeris, Diameter, vt minus legmentum. rnq nn o, 0 00 00
Maius Tegmentum. 3 2 3, 6 c <3, 797.73
Dimidium maioris Tcgmeti. Latus Quadrati dextanti circuli aqualis, vt Tota. ^ I 61,003, lg. Lf .E-
Minus Tegmentum.
Summa. Latus Qua drati dextanti circuli asqualis, Tedum proportionaliter &
concinuatumminore legraenco.
Diameter, vt Tota.
Maius Tegmentum.
Semidiamccer.
Maius Tegmentum Diametri continuatum dimidio totius, potens ideh quin-
cuplum eiuTdem dimidij. Latus Quadrati equulis dextanti Circuli ledo
& continuato vt Tupra.
<3l, 803 , S 98 .SS
Z13, <30^, 797.7 8
^ 100, 000,11?!
113 , 6c6 3 797.78
1 00, eoo, °°°>°°
21 3 , <3 0 < 3 , 797._7 j
RVRSVS IN Numeris ,
Potens TeTquialterum Semi-diarnetri. Aggregatum Sinus Peripherie xv. &
linus lxxv.Relidue. Aliqua Tota continuata minore Tegmento.
Minus ideo Tegmentum.
Tota vero.
Latus autem Quadrati quadranti circuli equalis.
Confintiunt in tot figuris quot contentus efl Mathematicus Canon .
122, 474,±Ll_1L
• 33 , 8 ji,iiw±.
88, 6 z 3, 171*1
88, 623,
H
5*
FR. A NCISCI VIETjEI, vniversalivm inspection vm
E sto igitur piper g centro deficriptus Circulus a (2 y 7, quadrifieflus a duabus Diametris
ct i y, & |3 s L Et in ct e y Diametro capiatur ab e centro linea t [i, longitudine
y r vel t S' [emi Uteris quadrati circulo infcripti. Et a @ angulo fimicirculi ducatur
per [i punflum linea @ p. a . Et fecetur radius g ^ media, & extrema ratione in y
punflo s &fit g v minus fegmentum , y 7 maius. Et ab y ad /u, ducatur Unca ijl y, cui
ab g centro fiat parallela pe- Vt g y efl minus figmentum t J\ ita p p>, efl minus
fegmentum tetius $ p :& ideo @ p Tota potens Quadrantem Circuli. Qua fi dupletur
in as punflo erit $ es latus Quadrati toti Circulo aqualis. Miliies accuratior Tetra*o- fi
nijmtcs, quam vel ab Archimede, vel alio quopiam ha flentes adnotata.
22. VTI Sefltor quilibet commode quadretur, modo ratio
Perimetri ad bafim Sectoris non ignoretur,
^ANALOGIA. *
*
Pcripheria
Quadrans circuli.
Circulus.
Pcripheria
Quadrante minor.
Circulo minor.
Potentia adSemidia-
metri potentiam
Scfquialtera.
Sextupia.
Potentia Lateris cotinuati
minore Tegmento, asqua
AreasScdoris.
£ s t o igitur a.(6 Linea potens Semidiametri Scfiquialterum, Sextttplumut dati Circuli fuper qua, vt radio fleferibatur Circulus
& fecetur & g Diameter fecudum rationem data bafios Se floris ad quadrantem vel ajfim ' J
Perimetri ,velut in g punflo ,vt fit A t ad flenti quadrans Perimetri ad Bafim fi flo
ris. Et ducatur Perpendicularis fiub g pun flo fecans Pcripheria in y,ad quod educatur &y
fecans Diametrum (zv diametro orthogonam, in puflo J\ Erit latus Quadrati
an& fe floris datx continuatum minore figmento. Vt enim quadratum ocftad quadratum
&JV, ita cl i ad g^ injpeflione xv. in Mificellaneis Planorum.
Porro dato latere Quadrati are<e Se flor is aquali, datur Refla Linea aqua bafi Se floris
cum inter tam & dimidium radsj Latus illud fit proportionale , ’ ^
2 j. LATE LfiA Quinque regularium cor [orum
wfcriptorumSphara.
V
p
A l i y M Diameter Sphaerse.
T a l i v m Latas Pyramidis, Teu Tetraedrh
Latus Cubi, Teu Exaedri.
Latus Odaedri.
Latus IcoTaedri.
Latus Dodecaedri.
Latus Icolaedri efl: latus Pentagoni ci Circulo infcripti ,
cuius Diameter in panibus Diametri Sphaera: eft
Latus Bi- C ___
nonnae 9 Mj n ^ s> g o, 000 , 000 , 000 , 000 , 000 , 000 , id eft
Summa ideo vt s .
Latus Dodecaedri eft: maius Tegmentum lateris cubi, C
videlicet. s
C Minus
L* 4 °j 000, 000, 000
L. 2 .6, 666 , 666 , 666,-
h* 1 3 5 3 3 3 , 333s 3 3 3 >7
L. i0 3 000, OOO, OOO
L. 11,055,728, 090 *»vrct
L. 5,092,880,146 wr *
L. 3 2., 000,000,000
- — 2 0, OOO, OOO, OOO
944, 2.71, 910
11 , 055,728,090
L. 1 6 , 666, 666, 666 ~
L- 3> 3 3 3> 3 3 3 5 3 3 3 i
200, OOO, ° 00 ’ 00
163, 299,
1 1 5 , 470, CLL . Z ±
I 4 I, 4 2 I, Hg.H
I95, 146,
7 1, 3 46, hzl *!
178,885,
I 2 9 , ®99) OrAeQe-
57 , 735 ,
Summa 7 I, 3 64, 4 - 17 . 9 *
AD CANONEM MATHEM ATICVM, LIBER SINGVLARIS.
5 ?
24.. DFFL ICAT IO Cubi
Si fiet quatuor Reto continue proportionales 5 quarum Quarta fit dupla ad Primam potentia:Erit Ter-
tia , vt Media proportionalis inter Potentem Re&angulum fub mediis vel extremis contentum , &
Quartam, continuata vigefima parte Quartae tyyvTcb.
V x ex ferie continue proportionalium inter Semi diametrum & Diametrum ,<& earum Diagrammate • Cupra adnotatisfunt
continu e proportionales.
I.
<x |3
141, 421 2J5
L. 20 , OOO, OOO, OOO
Latus Quadrati Circulo inferipti.
IU III.
cte cL-y
& earum numeri Canonici.
158,740125, 178 , I79 74 - 4 -
mu
etsr
200,000
L. 4 ? OOO, 000,000
Semidia meter
Proportionalis vero media inter latus
Quadrati inferipti &; Diametrum.
Z 1 1
168.179 _
I O, OOO 000
178. 179 Ili.
C0NSENTIVNT1» tot figuris quot contentu a ejl Mathematicus Canon.
Vigefima Diametri.
Summa.
- - « «. / C, — yr”p g->r '7
et v produdione y 0 qu<e Jit vigefima pars Diametri , ^7* a puncto a, in perpendicu-
lari ) c y ideo protradd, adfumatur a, £ longitudine ct 0, fiecans P eripheriam in pun-
do y. Erit cl y Tertia proportionales, & g •vero Secunda , ex qua ideo Cubus erit du-
plus ad Cubum ex & (3 Prima , fiicuti & & Quarta proportionalium dupla ejl ad
a (i Primam.
Vigesima autem pars Diametri commode cop aratur ex repetita figura redudio-
mt linea Redae, ad Peripheriam. Vbi @ g ejl fefquiquintum ad dimidium fiemidia-
metri,Q P' vero dimidium. Differ entia itaque inter. ^ (3 $ ejl decima Semidia -
metri, feu vigefima Diametri.
DvPLlCATio Geometrica & arti fciofa , non fortuita vel Mechanico indigens ,
qua , etfi non fit accurata , attamen non data ejl hadenus accuratior. Qua enim
circa idnegocij cotulit Orontius,ea prorjks funt mere nugxfuam ■fvjSbygtvpicLv pro-
dentibus Canonicis Mediarum proportionalium numeris, adhibita methodo dodri-
n& Triangulorum . .Accurata certe frujlra ex arte quaeritur . Vna enim ope- &
ratione duo principalia media non adfequitur Geometra, fed vnum tantum. Itaque
geminus cafus fortuito & hmyyas adftmilddus ejl , aut ad auxilium duorum Gno-
monum, vel Paraboles cum Hyperbole , vel binarum Parabolarum, aut adM efiola-
bum Platonis, Hieromfue,aut aliud Mechanicum recurredum,& in hoc negotio[vt
ante de Tetragonifmo Circuli monuimus)labori deinceps parcendum .
w
6° FRANCISCI VIETIE I, VN I VERS ALI VM INSPECTlONVM
D EMO N ST K ATIO LIMLTVM ANALOGITE P ERI METRI
CIRCVLI ^4 D D IuiMETRVM.
M. D demonstrationem Analogia Perimetri Circuli ad Diametrum proponitur Tabella hac. -j-
A n g v l x, Trianguli
aequi lateri Subdiuiho-
nes fcptedccim in duas
parces aquas.'
$ V B clt tt i' fio P enp h er! rt
Numerus uterum
Polygoni deferipti
circavel intra cir-
culu, ad duplum
Peripherie.
Numerus idem quadratus.
Smiu
Cum notu exceffus er
dejicienti*.
Sinus Bafeon.
i
Pare. Scrup,
50, o
5
'3 *
Latus Quadrati.
2, 500, 000, 000
Latus Quadrati.
7 5> 000, 000, 000
ii
15,0
I 3
T 44
559 , 872, 2 fere.
559 , 872, 981 er Amp.
—
9> 3 ?©> 127, 018 cr4,7!p.
9 , 3S©3 127, 01944.'
m
7i 3 ©
■. 34
57 *
170, 370,859 fere.
17 0, 3 70 , 858 | cr-oap.
9, 829, 529, I 3 I er amp.
9, 829, 52 9, I 3 I {fere.
mi
3>45
48
3, 304
42, 775, *94/«A
4 2 > 77 5 » *9 3 er amp.
9, 9 5 7 ’ 2 2 4 ’ 3 ©* ^
9 , 9 5 7 ’ 2 24, 3©7 M
V
i, 53 f
95
9> 215
IO, 705, 3 84 /ere.
IO, 705, 3 8 3 7 0~ amp-
9 , 989 , 2 94’ 5 l 5 er amp.
9, 9® 9, 294, 5 l 5 i/erc.
VI
5 *?
193
3 < 7 , 8(74
2 > 677 ,QG 3 - fere.
2, 577, 052 £Tamp.
9 > 997 ’ 3 22 > 937 ertmp.
9, 997, 3*2, 938 feri.
VII
o, z 8 {
384
147,455
559 , 3 1 1 fere.
**9, 3IO er Amp.
9, 999 * 3 3 °, 689 er amp.
9,999, 3 5 ©5 590 'fere.
VIII
o, 14 A
758
5 89, 824
1*7, 33I -fire.
1 57 , 330 er amp.
9, 999, 832, 559 cr amp.
9, 999, 832, 570 fere.
IX
0,7 A
H
w
vA
<?\
2, 3 59,295
4I3 83 3 /«4
41, 832 & Amp-
9, 999, 95 8, 157 er*»p.
9 » 999,9 5 8 > 1*8 fere.
X
°> 3 n
3, 072
9 > 43 7 >i 34
10,459 M-
10,458 & Amp.
9, 999, 989» 54 1 er amp.
9 , 999 , 989 , 54 2 M
XI
O, Ittt
*, 144
37, 748, 735
2 , 5 15 /«r.
2,514 er Amp.
9, 999, 997, 3 8 5 er amp.
9, 999 . 997, 3 8 * M
XII
O, O rji
12 , 288
150, 994, 944
6 5 4 fere.
6 5 3 er amp.
9 ’ 999 ’ 999 ’ 54 * <«»/'•
9 ’ 999 ’ 999 ’ 34 7 /"*-
XIII
O, O fff
; 24, 5 7*
*© 3 » 979 ’ 77 *
16 2 £r amp.
XIIII
Oj O i 5 0T4
49 > 15*
2,41 5, 919, 104
4© er amp.
XV
^ _ 215
©J © :jo48
98, 304
9, 553, 57 5 , 4 1 5
I O & amp.
XVI
L» 5 w 4, o <> (j
195, 5 q 8
38, 554, 705,554
2 CT amp.
XVII
o, O
393, 2 1 <7
154, 5 i 8, 822,555
0 er amp.
*
)
AD CANONEM MATHEM ATI CVM, LIBER SINGVLARIS. e.
; ■
Facundi.
Cum notis excejfus
dejicienti a.
Facundi Bctfeon,
Cum notis dejicientia O*
excejfus.
Hypotemfe Bafeon.
Cum notis deficientia cr
excejfus.
Latus Quadrati
1 3 = 333 = 333 = 333 y
Latus Quadrati
3 0,0 0 0,0 0 0,0 0 0 Accurate
Latus Qimdrati
40, OOO, OOO, OOO accurate.
717, 957, £99 /er/
717, 9 £7, &9J & amp
139,282,032,301 crdinj
139,282,032,303 fere.
149, 282, 032, 30I CTamp.
I49, 28 2 , 032, 303 fere.
I73, 323, 80Z fere.
17 3, 323, §00 Crrfwp
57^,954,803,402 CT/imp
57<J, 954, 805, 412/ere.
5 86, 9 54, 805, 40 2 cr Amp.
$86, 954, 805, 41 2 /ere.
4 a = 9 5 9=45 7 /^-
42, 9 5 9 = 45 5
2,3 27,77<5',2<5'2,I 5 I creimp'
2,3 27,77«?, 2^2, 193 /«*•
2, 337, 77£, 2 £2, 15 i crrfw/.
2 > 5.5 7 , 77 <?= 2£2, 193 feri J
IO, 71 ^) ^20 fere.
IO, 7 l£, 8 I 8 tr Amp.
9,3 31,094,3 3 1,784 ©-»«»/>.
9=3 3 *=o 94=3 3*=9 54 M
9 = 54 r = 094= 351= 784 cramp'
9 , 34 T = 094, 331, 954/ere.
2, <?77, 780 fere.
2-, £77, 778 cr <««/>.
3 7 = 344=3 74 =^ 49=3 5 ^ er *»*/=.
3 7 = 344 = 374=^5 0,0 3 8 /er/
3 7 = 3 54 = 3 74 = ^ 49 = 3 5 ^ er amp.
3 7 » 3 54 = 3 74=^5 0, 0 3 8 feri
££9, 3 56 fere.
66 9, 3 54 (T Amp.
149,3 97, 497, 928 , 0<58 CTrfW/.
I 49 = 597 = 497=9 5 0 = 798 M
149,407,497, 928, 068 Cramp.
149,407,497, 930, 798/er/
I £7, 3 3 8 /er/
1^7, 33^ CT Amp.
S 97 =^° 9=9 9 1 = 544>9 54 cramp.
597,509,991,55 5,855/ere.
597, £19, 991, 5 44, 934 cramp.
597 = 619. 991= 5 5 5 = 8 5 £ /re.
41, 834 fere.
41, S 3 2 &Amp.
2,3 90,45 9,955,1 3 7,902 cramp-
2,390,45 9, 955 , 181,592/ere.
2, 390, 4£9, 9££, 137, 902 cramp.
2, 390,4 £9, 9££, l8l, 592 fere.
IO, 460 fere.
10, 45 8 CT Amp.
9, 5<?i, 859, 8^4,541, 148 er«w/
9, 5 £1,8 5 9, 854, 7 15, 910/er/
9, 5£i, 8 £9, 8 £4, 541, 148
9, 5£i, 8£9, 8£4, 715, 910 /ere.
2,616 fere.
2, £14 C 7 -'
38,247,45 9,45 8, x£ 1,975 er
3 8,247,45 9,45 8,85 1 , 025 /ere.
38, 247,459,458, i£i, 975
38, 247,459,45 8, 85 1, 0 26 fere.
£55 /ere.
£53 & Amp,
1 5 2,9 8 9^8 5 7,8 3 2,547, 249 cr
152,989,857,835,443,45 I /ere.
152, 989, 857 , 832, £47, 249
152, 989, 857, 835, 443; 45 1 /=r/
I <74 fi r ' c ’
£11,959,451,3 30,588,832 efaM
£11,959,451, 341,77 3,«?4I /ere.
6 1 1, 9 5 9, 4 £i, 3 5 O, 5 8 8, 8 3 2
£ll, 959=451, 341, 775, 64.1 fere.
4 2 fere.
2,447,8 37,825,322,3 5 5,28 6 (?’amp.
2,447,8 37,82 5, 3 £7, 094, 5 24 fere.
2,447, 837, 835, 322, 355, 285 er-vwp.
2, 447, 8 3 7, 8 3 5, 357, 094, $2$ fere.
I I /ere.
9, 791,3 5 1,3 2 1,289,42 1,1 3 3 CT4?»p.
9,79 I, 3 5 I,? 2 1 , 46 8, 3 7 8,0 8 £/er/
9 = 791= 3 5 £= 3 3 1, 289, 42 1, 1 3 3 cr*»/\
9= 79*= 3 5 r» 3 3 1,458, 378, 086 fere.
4 /ere.
3 9=1 £5, 40 5, 3 05, 15 7, £84,5 28 CT Amp,
3 9,1 £5, 40 5, 3 05, 8 7 3, 5 12,342 /ere.
3 9 = i £ 5 = 4 ° 5 = 3*5 = M 7 > <^84, 528 cramp.
39, 155,405, 315, 873, 5 12, 342/ere.
I fere.
I 5 £,££l,£a I,240,£ 3 0,7 3 8,1 1 1 er amp.
I 5 6,661,62 1,243,494,049,3 £8 /ere.
I 5 £, ££l, £2 1 , 250, £30, 738, III cramp.
I $6, ££l, £2 I, 25 3,494, 049, $68 fere.
..
FRANCISCI VIET JEl, VNIVERSALIVM INSPECTIONVM
1 ~ ^ ^ qua Syntaxis feriei F acundorum Bafeos ita fi habet. A dgregantur Quadrata F acundorum & Hypotenufa Ba~
jeos Peripheria. Adgregata duplantur 5 cfT aufertur Quadratum Facundi dimidia a duplo 3 'Vt prodeat Quadra-
t um Facundi Bafeos dimidia.
Ad N ota.Tvm enim efl fupra Facundum Bafeos dimidia e (fe Facundum 3 & Hypotertufam Bafeos integra
adgregata. Et datis figillatim duorum laterum Quadratis 3 datur ex Arithmeticis Quadratum Laterum adgrega-
t orum 3 cum data Quadrata fingula adduntur 3 cA duplantur 3 & a duplo aufertur ipfa Later um differentia qua-
drata /vt fi dentur duo Quadrata 3 Dnum 4. cuius Latus efl 1. Alterum 25. cuius Latus 5. Horum Quadra-
torum fiumma ejl 2,9. Duplum 58. Ip forum autem Laterum differentia 3 , cuius Quadratum efi 9. Si igitur 9. au-
feratur a 58. prodibit 49. Quadratum lateris 7. adgregati e duobus.
D e n IQ3E Quadrato Facundi Bafeos 3 additur Quadratum Sinus Totius ad confutuendum Quadratum Hypo~
tenufa.
N o T a E liero excejfuSj njel deficientia ita confiituentur certo. Quadratis Facundorum Bafeos 3 & Hypotenufa in
bificlione anguli Trianguli aquilateri adgrcgatis & duplatis 3 aufertur Quadratum Facundi dimidia fuperans
lufium 3 'vt prodeat Quadratum Facundi Bafeos dimidia deficiens a iuflo 3 & e contra 3 aufertur defciens 3 r vt
prodeat excedens.
De iNCEPs adgregantur Quadrata Bafeos 3 tum Facundi 3 tum Hypotenufa fimilis nota. Et fi excedunt iufium ^au-
fertur Quadratum F deundi dimidia deficiens } & prodit Quadratum Facundi Bafeos dimidia 3 multo magis exce-
dens „ cum a fummd alio qui excedente nihilominus ablatum fit Minus a quo. Et fi deficiunt aggregata d iuflo 3
aufertur Quadratum Facundi dimidia excedens 3 & prodit Quadratum Facundi Bafeos dimidia multo magis de-
ficiens 3 cum d fummd alwqui deficiente rurfus ablatum fit Plus aquo.
Qz A DRATA Facundorum Peripheria excedentia^uel deficientia comparantur e Quadratis Sinuum excedentibus
'vel deficientibus 3 methodo mox particulatim exponenda & demonfrandd pofi generale Theorema 3 quod nonin-
conuenienti ordine prafiat imprimis adnotajfe.
FlCVND vm l>idclicet dimidia minorem ejfe dimidio Facundi integra 3 njt in figura ad Analogiam 3 quam dixi-
mus M rchimedaam 3 adfcriptd 3 M C minus efl A M. Sinum r uero maiorem 3 quia ratio Peripheria ad Peripheriam
maior efi ratione Sinus ad Sinum.
ITA qjv; E cum datus fit Peripheria l ~ aenius fcrupuliF acudus L. 65 A excedens iufium, multo magis ad Peripheriam
—^excedet Facundus L. 163 ^ dimidium L. 654, Et cum Facundus excedat pmulto magis excedet Sinus f ea-
rundem conflituatur partium, ,cum femper minor fit Sinus F acundo.
E T cum datus [it eiufdem Peripheria Imius fcrupuli Sinus L. 6<rf deficiens a iuflo 3 multo magis ad Periphe-
riam ~ deficiet d iuflo dimidium lateris 6 ^] , Et cum Sinus deficit 3 multo magis deficiet Facundus } fi e ar undem
conflituatur partium 3 cum femper Facundus excedat Sinum,
AD CANQNEM M ATHEM ATIC V M, LIBER SINGVLARIS. 6
articularis autem cJMethodus 3 qua comparata fuerunt Quadrata P acundorum JJla fuit.
Semi - latus
Poltgont
laterum.
6
Qualium , quadratum Sinus] Talium quadratum Sinus
Refidua: j Pcriphcrise.
7,5 00,000,000 accurate 2,$ 00,000,000 accurate
Qualium igitur
'10,000,000,000 rfeew.
Talium
3,3 3 3,3 3 3,3 3 3 f
„ 12
9,3 30,127,018 cramp.
9,3 30 , 127,019 fere.
669,87 2,982 fere.
669, 872,981 er<*wp
717,967,698
9.5 jo,ji7,oiS|»/<».
7I ~
/ /j?' /, y / 9 J? j o,I 17,0 x 9i uframp.
24
9,8 2 9, <J2 9,1 3 I cramp.
9,8 2 9,62 9,1 32 fere.
170,370,869 fere.
170 , 370,868 CTrfwp.
E7 3,5Z3,8ox 6 ^ 7i ^ oS9
' J * J 9,819 619,1 j 1
173,523,800 f,15I ’ 0 " 8;+o --
48
9,957,224,306' cramp.
9,957,224,307/fn?.
42,775,694/^.
42,775,693 CT^wp.
42,959,456
r 9,977,11+, 306
42,959,455
r > J -1 3 > 9 , 977 , 114,507
9 *
9,989,294,6^1^ cramp.
9,9 8 9,2 94,6 1 7 fere.
10,705,348/em
10,705,347 er-<wp.
IO ' T l6 8^0 7,67},55 ’ s - 88 °
3 3 9 989,19+, 6 TfF
10,716,819 7 ’^ 1 ’ 9?<w
^ 9 9 S 9 , 19 +,S 17
192
9,997,^2 %, 957 cramp.
9 , 997 ^ 21,938 feri
2,677,06 3 /ere.
2,677,062 Cramp.
2 , 677,779 8 ’ y8 i’ o8 3>°77
1 9 , 997 , 3 H ,937
2,677,778 8 ? 77 ’ 7t3 ^ 5 <r
9 , 997,3 11=93 3
384
9 , 999 , i 30,689 cramp.
9 , 999*3 i 0,6 90 fere.
669,511 fere.
669,3 ^ c cr
669 255
3 3 9 , 999,5 50,539
669,354 8 ’°°*- ?1 *’ 7 * 0
r 9 , 999,3 3 0,690
768
9,999,832,66$ cramp.
9>999>832 ,666 fere.
167 , 33 % feri
167,3 34 cramp.
167,337
7 * ' 9 , 999,3 3 1,66 y
167,3 36 s ’° 0I ’ ool ’ li i:
^ 9 , 999,8 } 1,666
l,S$6
9,999, 95 8, 167 Cramp.
9 > 999>9 5 8,168/ere.
41,83 3 /ere.
41,8 3 2 CT amp.
si
4I,8?3 1 , 7 + 9 , 999,889
J 9 , 999,97 8,167
41,8 3 2 1 ’ 749 ’ 9I *’* i *
“ 7 9 , 999 , 97 8, 168
3,072
9 3 999 3 989 >f 41 ei^wp.
9»9 9 9>9 8 9, 5 42 /ire.
10,45 9 M
1 0,45 8 CT amp.
10,459 io 9 , 5 r ,<r81
~ j ^ 9,999,989,7+1
T ^ .. „ 0 * 0 9, 5 69,76+
9,999,989,7+1
Gi 44
9 , 999 , 997,3 8 5
9,999,997, 3*6 f er ' e -
2,6 1 5 fere.
2,6 14 Cramp.
2,615
1 9 999,997,387
- ^ 6, 8}1, 996
z?OI 4 9,999997,586
1 2,2 8 8
9,999,999, 34 *
9,9 9 9,9 9 9, $ 4-7 f er '-
6 5 4/ere.
653 cramp.
654 4l7 ' 71 "
‘ 9,999,999, 3+S 1
£•-. +16,409
5 7 9,999,999,347
COMMENTI fitit quidam Pentagoni circumfripti ad inferiptum rationem efie fifiquialteram, Hexagoni 'fifqui tertiam, Heptagonififquiquartam , CT ita m
infinitum, firuato eodemprogrefiionis erdine.Latcra itaque cr Semilatera in eadem ejfent ratione, potefateiFacundufique cr' Smus.yCt non filum fimm com-
mentum non demonfrantfedfalf fimum ejfe ratio numerorum conuimit.
V-M
64 FBLANCISCI VIETJBl, V N I V E R S A L ! V M INSPECTI ON VM "
Quadrata ero Sinuum Minora Maiordquc Iteris ita fuerunt elicita , Ac primum.
QJRADRATA FERIS MAIORA , RESIDFARFM VERO
CONSE j Qf E N T E M l N 0
S cmE latu*
PsljjfMt L(-
terum.
6
Quadratum
Sinus totius 10,000,000,000
Quadratu Sinus
Peripherie 30 2,5 00,000,000
Quad. Refid. 74 00,000,000
Sinus ipfe 86,60 2
Verfus 13497
Dimidius 6,69$
5 4 °, 3 7 crump.
4 5 9 >6 y f crc -
7 x p , 8 z j«r.
Otii qmdru-
tu* efficit di*
tdXAt
i
j
7,499,999,998 l$ 3 , 74 » 79 » 73 »tf*
12
Quadra. Sin. I 5 6 69,87 2,98 2 fere.
Reiidua: - 9, 3 3 0,1 2 7,0 1 8 0* amp.
Sinus ipfe 9 < 5 ", 592
Verfus 3,407
Dimidius 1,703
582,6^ c?"
4 I 7,3 8 /ere.
708,65) fere .
9 , 330 , 127,017 (20,1 5,26,06,44
24
Quad. Sin. 7, 3 O 170,370,8 6 ^ feri
Rsfiduse 9,8 29,629,1 3 I crtmp.
Sinusipfe 99,1444 8 6, 1 3
Verfus 855 j 51 3,87 fere.
Dimidius 427 ( 756 , 9 ^ 4 ^-
9,829,629,129 [p 8 s i 7,62,3 7,6p
4 S
Quad. Sin. 3,45 42,775,^94/^.
Kefiduas 9,9 5 7,2 24. 3 0 6
Sinusipfe 99,785
Verfus 214
Dimidius 107
8 p 2 , 3 2 «5T
107,68 fere.
053,84 /err.
9,9 5 7,2 24,3 0<7 ! 0 p, 8 6, 3 4 ,p 8,24
9*
'
Quad. Sin. 1,5 2 t 10,70 5,5 8^. feri
Rciidue 9,9 89,2 94,6 1 6 crvnp.
Sinusipfe 99,94614 5 8,74 or
Verius 5 3 j 5 4 1 ,z 6 feri
Dimidius 16\ 7 7 0 , 6 3 jfrrr.
9,989,294,1714166,65,22,3 8,76
192
Quad. Sin. 0,5 6 ~ 1,6 J J ,06 $ fert.
Reiidue 9 . 997.3 ia >9 3 7
Sinusipfe 99,986
Verfus I 3
Dimidius 6
613,7 p CTAfnp.
3 8 6, 2 I fere.
6 p 3 , 1 1 fere.
9,997,3 22, 9 37 1 p,o 6,1 8,1 6,41
1 6 4
Quad. Sin. 0,2 8 \ 669,311 fere.
Refiduse 9 . 999. 3 3 0,6 89 cc
Sinusipfe 99,996
Verfus 3
Dimidius 1
65 3,3 9 cramp.
3 4 6, 6 1
673,31 /er*.
9 > 999 >$ 3 0 ,< 589 ‘!op,p 7 ,p 8,4p,2 1
768
Quad. Sin. 0,1 4— 167,3 3 1 fere.
Rcfidua; 9,999,8 3 2,(559 CCAtnp.
Sinus ipfe 99,999! 1 63,34 (sr
Verfus 1836,66 fere.
Dimidius (418,33 fere.
9 , 999 , 832 , 6(781 7 9 . 99 .P 9.9 5.5 6
Quad. Sin. 0,7 7x 41,833 fere.
Rciidue 9,999.9 S 8,1 7 cr ^»»7.
Sinusipfe 99,999
Verfus
Dimidius
7 p 0 , 8 3 cr *mp.
205,17 /rn*.
1 °. 4 i 5 9 f ,r ' g °
9>999>9 5 8 > 1 ^!°4>3 7>5 :t > 0 M 9
5.072
Quad. Sin. 0,3 1 0,4$ 9 f ere ’ ■
Reiidua 9 , 999.9 8 9,541 cr *m}>.
Sinusipfe 99.999
Verfus
Dimidius
947,7 ©
5 2,3 0 /h'6.
26,15 f e ™'
9,999,989,540 1 °o,2 7,3 5,2p,00
^,144
Quad. Sin. 0,1 ttt 2,6 I 5 fere.
Relidme 9 , 999 . 997.3 8 5 CTAtnp.
Sinusipfe 99,999
Verfus
Dimidius
p 8 6,p 2 CFdntP.
a e i
13,00 pwe.
6,5 4. feri
9,999-997,384 1 oo j0 i >7 x,o 8,64
12,288
Quad. Sin. 0,0, fff ^ 54 / f ^-
Reiiduas 9 , 999 . 999 » 345
Sinusipfe 99,999
Verfus
Dimidius
p p 6,7 3 & 4 mp,
3,27 fert.
1,64 fere.
9 , 999 , 999 , 3461 °o, oo ,i °,6p,2p
. .
AD CANONEM MATHEMAT ICVM, LIBER. SINGVLARIS. <T,
QJf ADRUAT A VERIS MINORA 3 R E S IT) V A RV M VERO
CONSE QJfi E N T E M ^€'1 0
ScmiUtu*
Polyeem Li~
tarum.
6
Quad ratum
Sinus totius 10,000,000,000
Quadratu Sinus
Peripherie 30 2,500,000,000
Quad. Sin. 'Rciid. 7,500,000,000
Sinus ipfe 8 6,6 021540,3-8 fere
Verfus I 3,3 9 7 459,61 cramp.
Dimidius 6,69 8 j 7 i 9, 8 1 er
Qjficjuadra-
tw efficit nu
meru mul-
to maiorem
dato, 'vide-
licet
!
1
7,5 0 0,000,000 | 2 6,9 5,3 0,5 4,44
1 2
Quadra. Sin. 15 669,872,981 er mp.
Reiidue 9,330,127,01 ^ fere.
Sinus ipfe 917,592
Verfus 3,407
Dimidius 1,703
5 8 1 , 6 3 /ere
4 x 7 , 3 - 7 er *»?/>.
708,53 \ CTAp.
9,3 30,127,019 1 1 3,3 3,77,7 1,49
^4
Quad. Sin. 7,30 I 7 0, 3 7 0,8 6 8 ~ amp.
Pvdidue 9,829,1729, 1 3 I y/m-
Sinus ipfe 99,144.
Verfus 855
Dimidius 427
1 4 8 8, 1 4 fere
5 1 3 , 8 6 er rfwp.
7 5 5 9 3 CTamp.
9,8 29, 6 2 9,1 3 I I 9 6,4 6,5 1,0 9,9 6
48
Quad. Sin. 3,45 42,775,693 ccamp.
Reiidue 9,957,224,30 J fere
Sinusipfc 99,785
Verfus 214
Dimidius 107
8 9 2,, 3 3 /ere
107,67 cr <<wp.
0 5 3 , 8 3 f er dp.
9,957,224,308! 09,43,51,81,89
96
Quad. Sin. 1,527 IO, 705,383 fcTAmp.
Retiduie 9,9 8 9,2 94, <7 1 <7 Ifere
Sinus ipfe 99,946
Verius 5 3
Dimidius 2 6
4 3 $,1 5 f er ?
541,15 er <<wp.
770,61 •O' amp.
9>,9 89,294,6x6' i 66,54,5 1,5 6,15
19S
Quad.Sin. 0,5 6~ 2,677,062 er amp.
Reiidue 9,9 9 7 , 3 2 2 >9 3 8 /ere
Sinus ipfe 99,9 S6
Verfus 1 3
Dimidius 6
613,80 /«•<?
3 8 6,1 0 ce amp.
653,10
9 , 997 , 3 22 > 9391 1 9 ,° 3-3 0 , 44 ,°°
384
Quad. Sin. 0,2 87 <7(79, 3 1 0 er amp.
Refidue 9 , 999-3 5 0,690 fare
Sintis ipfe 9 9,9 9 e 3
Verfus 3
Dimidius 1
6 5 3 , 4 0 fere
34 6,60 er
673,30 er dwp
9 , 999,3 3 0 , tf 9 l 1 09,97,3 I ,5 6,00
768
Quad. Sin. 0,1477 167, 3 3 0 CTamp.
Rcfldue 9 , 999,8 3 2,670 fre
•
Sinusipfc 99,999
Verfus
Dimidius
1 6 3 , 3 5 fere
8 3 6, 6 5 er
41 8,3 1 er <(wp.
9,999,832,6701 69,99,83,11,15
1,53^
Quad. Sin. 0,7 ~r 41,8 3 2 CT amp.
Reiidue 9 , 999,9 S 8,1 <7 8 fere
■
Sinus ipfe 99,999
Verfus
Dimidius
790,84 /ere
109,1 6 er amp.
x 0 4, 5 8 & amp.
9 , 999,95 8,168 | 04,3 7 , 47 , 9°,3 6
3,072
6,144
1 2,2 8 8
Quad.Sin. 0,3 10,458 cramp.
Relidue 9 , 5 > 9 9,9 89, 5 42 fere
Sinus ipfe 99,999
Verfus
Dimidius
547,7 1 fo*
5 1,19 cz amp.
1 6, x 4 er
9,999,989,542 | 00,17,34,14,41
Quad. Sin. 0,1 r H 2,6 14 cramp.
Refidue 9 , 999 , 997,3 86 /ere
Sinus ipfe 99,999
Verfus
Dimidius
9 8 6,9 3 fere
i 3 ,0 7 er amp.
6, 5 3 er d?wp.
9 , 999 , 997,3 86! 0 0,0 1,70,8 1,49
Quad. Sin. 0,0, 653 cr *»*/>.
Pvdidae 9 , 999 , 999 , 347 er fere
Sinus ipfe 99,999
Verfus
Dimidius
9 9 6 >7 4. fere
3,1 6 er
1,63 ce amp.
9 , 999 , 999,348 100,00,10,62,76
5
FR. AN CIS C I V I E T jE T, VNIVERSALIVM INSPECTIONVM
H i s ita certo conjiitutis ,Efto Circulas A CB fuper H centro defcriptus. Et Jit
B C Latus Polygoni infripti laterum 392 zi6 s (Sy angulus B A C ideo
part. ofcr. o-fff. Erit AB Diameter ad h C latusBd olygoni,vt L.i<q£ 3
66i 5 611, zty ftnjL ad L. i 5 o accurat e. Ad Polygonum vero ipfumJTt L.
15 6 5 661 , 61 i, z$yfiE>adL.iyy6 3 i8% 5 zz6y6,o accurate elyst L.
1563 661 3 6113 25,4 accurate, ad L. i 5 188,226, 56,0 amplius.
Qualium itaque A B Diameter adjumetur partium L. io, 000, 00O3
00 O3O accurate, Talium Polygonum ipjumerit L. 983696,0443007,*
& amplius. Seu Qualium Diameter ioo, 000 Talium EPolygomm yy }
J 59> t0^lm.Ueo<i ue Circulus , qui maior ejl Polygono infcripto, multo magis & amplius. Qui limes ejl
nonus ex pr finitis.
Alter non difjimih methodo ita defignatur.Ejlo rurjum Circulus Cy S z fuper
A centro defcriptus, &fit C B Scmi- Latus Polygoni circumjcripti laterum
?yjyi6Jdeoqj Peripherie Cypart. o 9 Jcr. o Erit A CadC h,Dt
L. 15 6 ,66i 36 21324,0 & amplius adL. i >0 accurate, Delyy t L.i^ 6^6 61,
621, 243 o accurate, ad L. i 3 o fere. Ideo que ad ipfum S emi Polygonum
circumfcriptum, vtL. 156,661, 621, 24, o accurat e, ad L. 1, 546, 188,
2263 563 o fere. Qualium itaque A C Semi-Diameter adfumetur partium
lo 5 OQO3 0003 000/ accurate. Talium S emi- Polygonum circumfcriptum
erit L. 9 8 , 69 6, o 44, 016, e fere , Seu Qualiu Semi-Diameter 100,000.,
Talium S emi- Polygonum circumfcriptum 514, 159, ff f f er ^- d deoque
Semi-Circulus,qui minor cf Scmi-P olygono circumfcripto, multo magis fere .
Brevi T abell.d adnotat e funt Peripherie in partibus Diametri ad fingulas partes quadrantis Circuli : & e regione inferte
linee ReBe congrue , tum infcriptejum circumfcripte pro trina ferie , numeris ad Millefima vjque partium propagatis t ad iujlam & be-
ne mmeroj&m Mathematici Canonis Epitomem.
ad cano nem mathematicvm, liber singvlaris.
07
'DEMON STRATIO L1M1TNM S I N.V S
V N I F s S C B^rv FLI-
EX eadem Tabella, Md Peripheriam part. o,fir-ififii fi m ™ ficrup. datur F 'ateundi Refidua Hypotenufia L. ^8
24 a.6q, 458^ S 6 i y oz 6 fere, in partibus qualium Numerus, Peripherie congruus, Ht Sinus Re Ai. OualiHm
itaque Hypotenufia L. io, ooo, 000, ooo 3 000, 000,00 Talium Sinus Peripherie pfife fer. erit L . 2,414,
5 3 z, o 5 8 3 34. & amplius.
Ex eadem, ad Peripheriam partium p,fir. o datur Fecundi Refidue Hypotenuja L. 141, 989, 867, $22, 4 47
249 & amphusjn partibus qualium Numerus Peripherie congruus , ut Sinus redii. Qualium itaque Hjypotenufi L .
io, eoo, 000, 000,0 o o, 000,00 Talium Sinus Peripherie , ~ jcr. erit L. £53, <>3 8, o 3 7, 3 3 JitE
Jr qv E ita Jo^/i f/ iwfcv A. 2, 614 531, 038, 34CO dwp/i^ ^ L. 453 3 8, o 3 7 , 3 3j Erk
^ t defendendo, Vt Peripherie ^ iif Maior ad minorem, ita Sinus ad Sinum cum nota deficientia .
-Er it itaque Ht L. 50, 615 ad L. i 4 , 384 ita L. 2, 614, 5 3 z, o 5 8, 3 4 eO amplius ad Z4846 1 3 9, 43 4, 63
multo magis & amplius, id ejl 29, o 8 3 , 3 1 5», 5 ^ eO amplius.
E t ajcendendo Peripherie }~ a d fifi Minor ad maiorem ita Sinus, ad Sinum cum nota exceffius.
-Erit z'ta<p? a/fL. 50, 625, ^ L. 45, 53 6 y ita L. 453, tf 3 8, o 3 7, 3 3 /v? L. 84 4 , 1 3 <>, 4 8 1, 00 multo ma-
gis fi ere, id ejl, 29, 088, 81,03 6 fier e.
4 >v oniAM a/m) inter Peripherie ±j£ O 0 fifiHnius ficrupuli , non omnino media ejl Peripheria fifi quefitafied hac
maior fi fi illa Hero minor fifi^ Differentia inter fimum maiorem & minorem inaequaliter fiecandaeft, fieruatd Ana-
logia, & maius fiegmentum addendum minori vera, vel a maiore minus aufierendum,Ht prodeat tandem Sinus vnius
ficrupuli fiatis accuratus.
Porro Sinu vnius ficrupuli fiatis accurate ita comparato , comparantur ex Analogia V infipeclionis xiff fimus duo-
rum ficrupulorum, deinde quatuor,posl ocloffexdecim, & ita continue duplando. Sinus vero ad tria ficrupula , vel ex
collatione duorum extremorum fiatis accurate conftituetur , ex quo deinde fimus elicietur fex ficrupulorum xij. xxiiij.
egy ita deinceps, donec Canonica feeries,gro inJUtuti ratione compleatur. ,_A T qv e HIC ES To TANDEM
EXPLICIT VS
VNIVERSALIVM INSPECTIONVM AD CANONEM
Mathematicvm, Liber Singvlaris.
/
69 |
ADDITAMENTA LIBRO VNIVERS ALIVM
INSPECTIO NVM i
^AD
£ANO NEM CMATHEMAT1GVM.
Ad Infpedion. ix. j
Analogia Periphcria: Circuli ad Diamctr umetis accurata.
Qualium
Talium Periphcria
Scmidiameter
Semicirculi
100,000, 0 0 0,0 0
314, 159, z<?5, 3 <S , i
31,830, <>88, 62
IOO, OO O, 000,00 \ JT
Deerant in libro hi poflrcmi numeri.
Linea prima.
A d caput. 5-Infpcdionis x v
in Ttnaunipoii Analogiis.
ij. ^Analogia tn duabtu lineis.
Linea fecunda.
Rcdtangulum fub lineis.
Quadratum e prima.
Quadratum e fecunda.
Rc&angulum fub lineis.
Deerant hi poflremi termini. Et fub
iitj. In tribus proportionalibus.
Extrema. Potens mediam &: dimidiam extremam ad-
gregatas,minus dimidid extrema.
Potens mediam & dimidiam extremam ad- Reliqua; adgrc*
gregatas, minus dimidia extrema. gars.
A d finem capitis 7 .eiufdcm"Infpedionis addi debuerant h xc verba.
D at a autem differentia, non adgregato , Quadratum dfferenthe additur ReElxnguU , &
conflatur Quadratum dimidij adgregati,vt vno Triangulo fit opus duntaxat, quale
fequitur.
cl (£ x/S etx
Adgtcgatumdimidium^ Differenda dimidia. Potens
Seu, Rc-ctangulum.
Differentia dimidia, plus
termino minore. , \
Consectarivm igitur generale ifiud ejh. Data vna e tribus proportionalibus, & adgrcgato
duarum reliquarum difeerni duas reliquas, si medix, ex ijlo Theoremxtefn extrema, ex enuntiato e quo em*
nauit ptflerior Analogia in tribus proportionalibus, videlicet, Redtangulum fub prima &c adgrcgato fecu-
dae 8c tertia; cum quadrato dimidia: prima;, asquari quadrato fecunda: &c dimidia: prima: adgrega-
d in fubieBd figurf. rbi g x prima, cum x d adgregato duarum reliquarum, Jit Diameter, O' bifecatur ex. in 1 8 puntfo, centro alius circuli.
. . . o/
0 >
Sjl enim vt ex ad % ita x ct ad x a.
Item vt A X ad x et, na x et ad x J N .
Et ideo erit vt ex ad Ax, idcjl ex plus Ae, ita x J'' ad xd, ideftxfr' plus j\».
Etper&tyoujficnvvttx ad A e, fu xJ\ sta ad
D i e S t item cap. 9. eiufdem InfpcSlioms , quod iam fequitur.
I
7 o
9 . %E G VL A , quam vocant, FALSI ’
Si dux proponantur linea a tertia quSpiam-dificnp antes, & nota fit adfieclioilUmm dificrepantiarumj, ejicientia finRan exceffus ,
ipfit etiam ratio deficientiarum /vel excejjmm inter jcflyel exceffus ad deficientiam, erit tertia Linea data.
Amlogid vnd Geometrica fieamdum quam operatio regula, quam vocant fid fi debuerat mjlitui & demonjlrari.
i „ , ^ n m mi
DifFeretia exccfluum , vel de~ Differecia linearum, In propriis Exceffus vel deficientia linea; Exceffus vd deficientia ciuf-
fidentiarum, In terminis terminis , vti adiurnptse primae vel fecundas, dem,
datse rationis vel fime. In terminis datas rationis. In terminis propriis.
Adgregatum exceffus cum de-
ficientia.
■Adjiimantur & (X An, lmea,CTefio vtraque deficit
DEMONSTRATIO.
ciens.
Vtraque excedens.
/
■4
-4
*
4
?/
<S£
♦
♦
-4
♦
*
*
■4
4
^4
/3 A
Cd
'""•nrn »»*»* •
*
♦
♦
£
*
♦
P \
'E
oc
F.
x
ac t- %
Qualium in linea jg defeflus efi A /x. Talium in linea ct 36 de fetius efixS^,
feu ce fx, quorum dijferentia \ ce- Ejl igitur \ ce Jicut g jc (id ejl tanta m fuis
partibus quantam partibus x (Z ejl t d) differentia mter datas,cui aqualis ce(p.
Erit igitur tota A /x Jicut ^ p.Addmua a, fZ, vt detur tertia linea quafita.
a se
^iltera dejiciens, Altera excedens.
Qualium in linea a, $ exceffus efi $ ^ feu ce /x, Talium in linea
exceffus ejl \ /x, quorum differentia A <o -Ejl gitur A ce Jicut g & differen-
tia inter datas cui aqualis (p: CT ideo erit tota A fl Jicut /x p, Ablati
ua ct x> vt detur linea tertia quafita.
w
\
4
•
4
'*
f • ■
*V
*
\
\
£
X
x
ot
fi i
'09
Qualium m linea & jg dejicientia [Z E feu \ jx, Talium m linea & x exceffus a [a,. Cuius adgregatum cum deficientia efi Rq-EJI gitur A a> fient g x feu A <p,
i deo que [x ce, vt /x p, Ablatiua <* x, vt detur linea tertia quafita .
IN- -ARITHMETICIS PARADIGMA.
Proponuntur duo numen I x CT 3 6, quoruvterque deficit a tertio quopiam ignoto. Qualiu autem defiet etia primi deprehenja ejl partiu i X , talium deficietia fe-
cundi deprehenft ejl partiu 8 ,vt pote hac ratiocinatione. Proponebatur ex fallo tertium illum numeru ignotum minutu fm dextate relinquere i rp.At \ x minutus fui
dextante relinquit x tatum,% 6 vero relinquit 6 .Hic itaq-^ deficit partibus 8 , qualibus ille deficiebat i x .Dfferetia vero inter 8 CT i x ejl 4 . Qualiu itaq., 4 aqua-
tur partibus x 4 , quibus difft irut data,talm 8 deficietia numeri fecundi aquabitur 4 8 partibus, addendis numero Jeeundo,qui ejl $ 6,vt confletur 8 4 tertius quafitus .
*/
7 i
Solita autem operationis ratio in regula falfi ejl huiufmodi.
Si qua linea feceturin tria fegmenta,Re< 5 tangulum fub tota & medio Tegmento Cum Re&angulo fiab extremis Tegmentis, sequatur Re£tan gu-
lo Tub adgregato primi & medij Tegmenti, & adgregato medij & extremi.
Sielmeaa.fi qua fecetur m pundis v cr P',Rcdangulum a,fl in y fi, cum Redangulo ^ _
ct y m fi fi aquabitur Redangulo et fi in y fi, Nt fi linea & (i, Jit 8 4 qualium a. y U.
1 z 14 48
yfi 14 Crfifi^d.Afimyfi videlicet 3 6 m 7 z efficiet z 5 9 z, quantum etiam efficit a. y m fi fi, id ejl, 1 z in 4 8, Cum ct fi in y fi,idefi, 8 4
m 14.
A fi enim in y fi per diarefim ejl a. y m fifi CT inJUper & y in y fi CT fi (i m y fi. Quibus tribus pofiremis Red angulis aquum ejl Reti angulum a fi ut otfi>
cum a. fi totius particularia figmenta fint cty, y fi, CT fi fi.
Nec interejl em limei re fica fit vel eurus . vt ,fi in Circulo aliqua Peripheria feceturin partes
tres, idem eueniet.
Sed & fi m Circulo infiribatur Qmdrilatemm a. yfi' fi, Refiangulum ex diagonfi ct fi in yfi aqua-
bitur Refiangulo fiubtenjk ct fi in fiubtenjam y fi CT Redangulo fiubtenfie ct y in jitbtenjdm fi fi.demonfiran-
teRtolemao cap. Q.hb.i.^yccNazwTU,^.
Sunt igitur
Proportionales
IN LINEAT SECT./T IN T R^E S P RJT E S, SITE
curua flue reda.
Primum & fecundum Tegmentum adgre
gara.
Subtenft primi &: fecundi legmenti adgre-
gatorum.
Diagonium vnum Quadrikt eri Circulo in-
feripti.
Medium Sc tertium Tegmentum adgre-
gata.
Potens duo Rectangula,
Vnum firb primo & tertio Tegmento,
Alterum Tub tota & medio,
IN s FPTEN S l S.
Potens duo Re< 5 t mgula.
Vnum Tub fubtenfrprimi &c TubtenTa tertij.
Alterulub Tubtela totius Se lubcefi medij.
Redangulafub lateribus oppofrtis alterne. Diagonium alterum quadrilateri.
SubtenTa medij & tertij ad gregat orum.
tt
fi
IN NOTIS .
Cct y in fi fi'
potens s ct
( -ct (i m y fi.
y ! 3
Et ideo p ex bis fex terminis vntts ignoretur ,ex reliquis dabitur.
Sed & fi y fc, fi ( 2 , y fi, non dentur in terminis fid ratio tantum eorundem, nihilominus datur tertia e reliquis ignota . & vicifiimfi & fi, ct y
efip et, fi non dentur in terminis, fiu Diagonia vna cum duabus inf criptis non oppofitis ,fid tarum ratio tantum, T ertia e reliquis ignota nihdomi-
nus dahitur.cum multiplicationes & diuifiones fiam per men furas homologas.
Secundum qu<e cum inpropofitaquxflione daretur linea a.y & a. fi in proprijs terminis, y fi vefio& fi & cum y fi earum differentia in
terminis data rationis, fi afafio ct, fi in yfi auferatur fattum ccy in fififiupererit Rettangulum yfi in ctfi,quoddiuifumpcr yfi dabit cl fi
qu&fitam.
E xcludebat ab Arithmeticis regulam falfi Petrvs R a m v s,quia imprudenter ea tra£fcabamr,&- fine Geometriat.luce. At iam caligine
fusa regnis quidem nomen , & ageometrica praxis ab exilio, quod ab homine AoyjcoTOT&iimperatum eft } nereducitor.Fun-
damenta vero, quibus ex arteinnittitur, retineantor } Sc extolluntor: & fecundum ea praeceptiones reguls , terminique arcte, latcvc
prsfiniuntor.
Ad infpc&ioncm. xix.
C A N 0 NI C jE Analogia Spharici ‘Trianguli re H anguli.
DECADIS J
JE
DECADIS II&
PENTAS PRIMA
PENTAS
SECVNDA
PENTAS PRIMA
Totus
Sinus
Sinus
Sinus
Totus
Faicudus
Farcudus
Sinus
Totus Hypot/*
Sinus Sinus I
I
C
A B
'A
CB
VI
C
AC
B
CB
mi
C
A
A &B ' |
II
c
AB
B
A C
VII
c
CB
A
AC
V
f
ii
c
CB
AB A&
III
c
A&
A
B'
VIII
c
AB'
CB
B'
C
AZ
AC B
IIII
c
<bb
B
A
IX
c
AB'
AC
A
iii
C
AC
B' A |
v
c
A Z
QfB AB'
X
c
B'
A
AB'
A
C
A
CB AB
i
1
1
SVE-V EC^DIS
i*
SVB VEC AT> IS IIM j
1
PENTAS
PRIMA ^
PENTAS SECVNDA
PENTAS
PRIMA.
Totus
Hypot.A
Hypot./* Hypot./»
Totus
Farcudus
Farcudus Hypotd*
Totus Sinus
Hypot/ 1 Hypor./i |
i
c
AZ
A
&B
VI
c
AZ
B
JBB
mi
C
B
A CB
ii
T
III
c
AZ
B'
AZ
VII
c
8%
A
AZ
V
f
II
c
&b
AB AC j
c
AC
A
B
VIII
c
AB
JCB
B
c
AB
AJZ B
11 II
c
CB
B'
A
IX
c
AB
AZ
A
III
c
AZ
B A j
1
c
AC
CB
AB
X
i
c
B
A
AB
I
c
A
SZB' AB j
fuit ordo Decadon & Pcnt&dw inmrfus m
Libyo ,
i
DECADIS II^ E
PENTAS SECVNDA
Totus
Hypor/“
Faecudus Faecudus
VIII
c
B
AZ
zz
VI
c
&£>
A
A£
X
c
AB
A
B
VII
c
A : e
CB
A
IX
c
A
AC
AB
V
III
f
ixii
i
ii
DECADIS III ^
PENTAS
r
PKIMA
PENT AS
SECVNDA
Totus Hypot /*
Sinus
Sinus
Totus
Hypot/*
Esecudus Fsecudus
C
A C
AZ
ZZ
VII
C
az
A
& B?
c
A
Z
AZ
IX
c
A
AB'
AJZ
c
CB
A
B
V I
c
SZZ
AC
B
c
AZ
C B
A
X
c
A B
B'
A
c
Z
AC
AB
VIII
c
B
CB
AB
S V B-D EC tAD I S I I ut
PENTAS SECVNDA
Totus
Sinus
Fscudus Faecudus
VIII
C
Z
AB
CB
VI
C
CB
B
AC
X
C
AZ
A
B'
VII
c
A C
&z
A
IX
C
A
Ai e AZ
S V B-D E C^i
PENTAS PRIMA
Totus Sinus
Fiypoc./*Hypotd
V
C
'AZ
AB CB
iii
r
c
A
B AC
i
mi
c
iZB
A %
i
c
AB
SZZ A
ii
c
B
AZ AZ
IS III-**
PE
NTAS SECVNDA.
Totus Sinus
i axudus paedidus
VII
C
A C
A
CB
IX
c
A
AB
AC !
1
VI
c
C B
A&
z
X
c
AZ
B
A
VIII
c
Z
&Z
AZ
^Ad Qaput 7. Infpecliom XX V .
Diameter Quadratum Diametri Circulus, &c.
a f 4, 547, 908, 94 2 oo,ooo»ooo,q©
127,323,954,47 100,000,000,00
'uit bt&c. numerorum feries in Libro. In ilici vero mendose adferiptus cjl numerus Circuli fubduplus inflo.
* 5 9,
1 12,
511
83 8
Error item efl in numeris ad Cubum analogis } qui ita fiunt refikuendi,
Qvali vi(
Cubus
Diameter
2 ; 1 55
2 ., OOO
O, OOO, OOO, OOO,
IO, OOO, OOO, OOO,
Cubus.
Talivm
Soliditas Spbte VX, Faff a Vidtt icet ex Spharicd. Superfuit;,
& *Di&metri Jextante,
4, 188, 890, 205
5, 23 5, 987, 75 6
64, o o
i- dmti.
o o
feri .
10, 0 o e
Arena
feri
ERRATA ALIA NONNVLLA- !
Fagina 1 j. legendum Ad i"”* 1 wn inficriptorum non 3 F m
P Agina 17. delenda fiunt hac verba, non. a matribus filias,^ reflitumd.i, non matrem ;\ filiabus. _ - . ,
Pagina %6 Juus numerus refiituendus efl. item m nolis Analogia capitis j. ubi legitur O B CC C B refiituatur G B £? J C G. Hem m fine pagina vh legitur
A O refiituatur A B.
Pagina 28. Linea Ad demonfirationem I. ut Quadratum cee, legatur *%•
■ Pagina 33 . vltimamta Illlf Analogi a efi e g O cr.
Pagina 39 Columnula penultima aaficribatur Analogia II H, non TUI*.
Tamu 4 4 numerus mendojus efi,CF congruus reponendus. Eidempagina mfcnbatur XXIIII ad numerum Infiechonis .
Pagina 50 XXV loco XXIIII.
Item, Sub nota A C fecunda Analogi a, S mus Refidui dlmidfiidejlfinus Complementi dimidia Jumma Piripberiarumadgreg/tarum.
Pannei 45 numerus mendojus efi,(y fiuus reponendus .Eadem pagina Jiib 1111 termino prima .Analogia rota fit y B. Nevero tn figura linea A C intelligatar cogi
tranfireperf Bionem line^ g v mpunSlo [/,. .
Eadem pagina Sub nota A C fecunda Analogi a, omijfa efl vox AiivAdix. Itaque fic legitor. Sinus dimidia; differentias Peripheriarum refidu x,id efi, Smus
complementi dimidia.
Pagina 47 ubi legitur,Duo confiituunturTriangula,deefi vox redtangula.
Pagina 4 8 deficiant punfta pofi vocem P L A^ I:& in perpendiculo Trianguli deficripti vbi legitur iQ' IT refiituatur -A D.
Pagina j-f numerus extremus efio 88, 6ir,non autem £> 3,6 23.
Vagina 55. Infinitorum laterum,id efi,x7mp(dv,numerofiorum.
Pagina 56. In Syntaxi Dugrammatos loco ^co 3 cty, & ot g, fubfiituendum efi. fi jSy CH fed nec omittendum efi fi \ & \y adgregatas ejfie Diametrum
ipfam auflam quinta parte.
In eadem legendum, Hic qualium.
Rurfus m eadem ,id efl; Diameter, erunt.
vagina 58 ad finem zi.capitisfigcndum.Longc accuratior Tetragonifmus.
In eadem, error efi m numeris lateris Dodecaedn,qui ita refiit nantor L, 5, 092,880, 145? iyyugzL 7 1 > 3 ^ 4 1 ' LZ, ~ L > numeris Uteris Cubi 1 15,470
75
ERRATA NONNVLLA IN CANONE,
OLXIX Scr. XXX~)
LXII
LXI
LX
\LIX
Sub ferte tertia m mfcnptionibtu numerorum ad partes afeendentes <LIIII
* ■ ./LUI
LII
LI
XLIX
(_XLVI
Vbi adfcnbenda fuerat pars LXXXI Ad lauam irrepfet numeru* L XXXV, ideo
emendandus
Et vbt XXX ad dextram irrepfet numerus XX VI II.
Itemfub parte XXXVII loco ferupul. XXXIIII repetitum efeferupulum
XXXIII
Numerus Facundus Perpendiculi fer. XXIII, itaefe reflttuejidus 66 9
Kmetathefes efe vocum Hypotenufa, Perpendiculum,^ altera in
\ alterius fetbroganda efe locum.
Numerus Hypotenufa Bajeos fer. XXI,
fer. XXII
Differentia rubra
fequens
Numerus Facundus Part.lll fer . XLI
Part. IIII fer. XXI
fer. XLVI
sinus Part. VIII fcrupulorum XIX
Dijfe. rubra inter Facundum Bafeos part .einfdem fjfe m
Facundus Bafeos Part. XI fer.V
16, 370, 324
15, 6 Z 6 , 229
744, °95
* 19 , 39 i
^457
7, 607
8,632
I 4»4^4
1,456
510,490
fer. VII
Facundus Bafeos Part. XV ferupulor. XIII
Facundus Bafeos Part.XXlll ferup.XXXV
ferup. XLI
Sinus Partium XXVII fcrupulorum XXX
fcrupulorum XL
Facundus Partium XXX ferupulor. XIII
Smus Bafeos Partium XXXI fcrupulorum I
Hypot.. Bafeos Part. XXXII fcrup.XXXll
ferup. LVI
Hypot. Bafeos Part. XXXIIII fer. XLIIII
Hypot. Bafeos Part. XXXVIII ferupul.' III
fcrup.V
ferup. VI
Sinus Bafeos fcrupulorum XXIII
Smus fcrupulorum XXVI
508,921
367, 2 17
2 18, 68j
215 , 025
4 *, 17 5
46,8 i 9
115, 743
85, 701 3
1 8 6, o 3 1
183, 938
I 44> ^ 5 9
162, 24<5
i#2, 125
162, 06 %
78, 369
62,160
ERRATA IN CANONI O.
Pag. 3 1. Numeri primi Bafeos non fuis fedibus collocantur. Primus afeendentium debuerat ejfe 1,351 .Secundus 1,360 .Tertius 1,3 6 S.aui primum locum oc-
cupamt. Incrementum ejlper oflonarium numerum, CT duo duntaxat vltimi fetis refpondent felidijs. Canonion pauca admodum vtilitatis . potior Ca-
non integer per Proftapharefes puras, <jua incedant per oBonanum numerum ,aut ottonano minorem . Is edetur propediem cum fer on: micarum In~
feefhonum libris.
IN CANONIO TRIANGVLORVM per jgaJyrafos.
Facundus Bafeos Partfe 57,17,23,4 6.
IN EPITOME MATHEMATICI CANONIS.
Facundus II partis
Facundus Bafeos eiuf iem
Hypotenufa
Smus V
Famnd.Perpend.
5, 240,777
I, 908, 113,671
I, 910, 732, 264.
8, 715, 574
8,748, 8 66
Facundus Bafeos
Hypotenufa Bafeos
Hypotenufa Bafeos VI
Hypotenufa Bafeos X
x, I43> oo $ ,2 2 2
x, 147, 371, 3x6
9 $6, 6 77, 224
5 75, 877,044
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M. D. LXXIX.
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